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On World Poverty: Its Causes and Effects

David A. Bessler*

November 2002

Abstract

Recent advances in modeling directed acyclic graphs are used to sort-out causal patterns among a set of thirteen measures deemed relevant to the incidence of world poverty. Cross-section measures of the percent of population living on one and two dollars or less per day from eighty low income countries are exposed to a battery of tests of conditional independence with respect to measures of economic and political freedom, income inequality, income per person, agricultural income, child mortality, birth rate, life expectancy, relative size of rural population, illiteracy rate, foreign aid as a percentage of national income, international trade as a percentage of national income and percentage of population that is under-nourished. Motivation for the method of analysis precedes results. Results are presented as a graph that shows our measures of economic and political freedom, income inequality, illiteracy and agricultural income to be exogenous movers of poverty when measured as the percent of the population living on two dollars or less per day. Foreign aid and international trade are not connected to the other variables in the graph. Results on our measure of extreme poverty (people living on one dollar or less per day) show that such populations are immune from improvements in economic progress of the general economy. The “rising tide lifts all boats” argument apparently doesn’t cover the extreme poor of our sample. Word count: 19 632. David Bessler (d-bessler@tamu.edu) is a professor of Agricultural Economics at Texas A&M University. Partial financial support for the work reported here is from the Food and Agricultural Organization (FAO) of the United Nations (UN). Results and implications, either stated or implied, are not necessarily endorsed by any of the above-mentioned institutions. Comments by Aysen Tanyeri-Abur and Tanveer Butt improved the paper. In addition, the editorial suggestions of Michele Zinn are gratefully acknowledged.

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On World Poverty: Its Causes and Effects

At one level of description it may be sufficient to say that living in poverty is a matter of chance,

related to the circumstances of one’s birth or the outcomes of nature or world events beyond an

individual’s influence. Apparently, none of us controls where, when, or if we are to be born.

And, once born, few (knowingly) choose to live in poverty.1 But people do live in states of near

or below subsistence levels. People suffer and die from such “living.” To affect change, one must

get beyond an agnostic understanding of poverty as a chance event and focus on the causes of

poverty. It is through the knowledge of such causes that we can (if possible) change outcomes to

a preferable set of realizations.2 Causal knowledge requires more than algebraic representation of

relationships among variables and/or their correlations in data.3

This paper studies causes and effects of poverty. It focuses on an inductive, rather than an

a priori, model of causation. A list of measured variables is specified without prejudice that each

is a cause of, an effect of or unrelated to other included variables in our list. Specification of our

list is based on recent writings on the economics of poverty and development (Sen [1981] and

reading contained in Chenery and Srinivasan [1988]). The paper is organized as follows. First we

review recent work on assessing causal relationships among a set of variables. This work comes

from efforts in computer science (Pearl [1995], philosophy and statistics, Pearl [2000] and

Spirtes, Glymour and Scheines [2000]) and mirrors recent applications in economics by the

1 Of course, there are those who do indeed choose to live in poverty. Particularly noteworthy are those religious communities whose members take vows of poverty. Such people may violate an axiom of rational choice, that more is preferred to less, if one does not include the perceived attributes of the religious life in the choice set. Other notable members of the set of people who appear to choose to live in poverty might arguably include artists (suffer for their art); but both groups, religious and artists, generally don’t live at the minimum possible state of existence, where many of their similarly positioned colleagues actually die of starvation or exposure to elements of nature. 2 See Russell (1948 ): “The power of science is its discovery of causal laws” (page 308). 3 Linear algebra is symmetric with respect to the equal sign, for example, we can re-write y = a + bx as x = -a/b +(1/b)y. Either form is legitimate for representing the information conveyed by the equation. A preferred representation of causation would be the sentence x y, or the words: “if you change x by one unit you will change y by b units, ceteris paribus.” The algebraic statement suggests a symmetry that does not hold for causal laws; as

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author and his former students (Bessler and Lee [2002], Bessler and Loper [2001], Bessler and

Akleman [1998], Awokuse and Bessler [2002] and Bessler, Yang and Wongcharupan [2002]).4

We follow our discussion of causality with a discussion of the variables considered in this study

and their support for consideration in prior literature. Results follow. Limitations of the study and

recommendations for future research on poverty and causal modeling conclude the paper.

Causal Modeling

One reason for studying causal models, represented here as X Y, is to predict the

consequences of changing the effect variable (Y) by changing the cause variable (X). The

possibility of manipulating Y by way of manipulating X is at the heart of causation. Hausman

(1998, page 7) writes: “Causation seems connected to intervention and manipulation: one can use

causes to ‘wiggle’ their effects.” Prediction of such ‘wiggling’ through intervention in

development is what gives many of us hope for improving the lives of those of us living in

poverty. A manipulation-based definition of causation is generally more in line with a

philosophical definition of causality than other recently offered definitions that focus exclusively

on predictability. For example, Bunge (1959) argues that causality requires a productive or

genetic principle that models "how something comes into being." X causes Y if X is productive

of Y. Definitions that focus on prediction alone, without distinguishing between intervention

(first) and subsequent realization, may mistakenly label as cause variables that are associated

only through an omitted variable. For example, Granger-type causality (Granger 1980) focuses

solely on prediction, without considering intervention. The consequences of such focus is to

causal laws are asymmetric. Finally, knowledge of a correlation between x and y does not imply causation, as both may be “caused” by a third variable z. 4 While we do not mention that the work on causality emanates from economics, its foundations are actually found in early papers by Simon (1953) and Orcutt (1952). We do not list these authors above because their use by economists has generally been with respect to an a priori model and not an inductive model of cause from empirical data.

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open oneself up to the frustration of unrealized expectations by attempting policy on the wrong

set of variables.

Directed Graphs

Essentially, a directed graph is an illustration using arrows and vertices to represent the causal

flow among a set of variables. A graph is an ordered triple <V,M,E> where V is a non-empty set

of vertices (variables), M is a non-empty set of marks (symbols attached to the end of undirected

edges) and E is a set of ordered pairs. Each member of E is called an edge. Vertices connected

by an edge are said to be adjacent. If we have a set of vertices {A,B,C,D} the undirected graph

contains only undirected edges (e.g. A B). A directed graph contains only directed edges (e.g.

C → D). A directed acyclic graph is a directed graph that contains no directed cyclic paths. An

acyclic graph has no path that leads away from a variable only to return to that same variable.

(The path A B C A is labeled “cyclic” as here we move from A to B, but then return to

A by way of C.) Only acyclic graphs are used in the paper.

Directed acyclic graphs are pictures (illustrations) for representing conditional

independence as given by the recursive decomposition

Pr( 1v , 2v , 3v , ... nv ) ∏=

=n

iii pav

1

)|Pr(

where Pr is the probability of vertices (variables) v1, v2, v3, ... vn, pai the realization of some

subset of the variables that precede (come before in a causal sense) vi in order (v1, v2, v3, ... vn)

and the symbol A represents the product operation, with index of operation denoted below (start)

and above (finish) the symbol. Pearl (1995) proposes d-separation as a graphical characterization

of conditional independence. That is, d-separation characterizes the conditional independence

relations given by the above product (APr). If we formulate a directed acyclic graph in which the

variables corresponding to pai are represented as the parents (direct causes) of vi, then the

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independencies implied by the product given above can be read off the graph using the notion of

d-separation as defined in Pearl (1995):

Definition: Let X, Y and Z be three disjoint subsets of vertices [variables] in a directed

acylic graph G, and let p be any path between a vertex [variable] in X and a vertex

[variable] in Y, where by 'path' we mean any succession of edges, regardless of their

directions. Z is said to block p if there is a vertex w on p satisfying one of the following:

(i) w has converging arrows along p, and neither w nor any of its descendants are on Z

or (ii) w does not have converging arrows along p, and w is in Z. Furthermore, Z is said

to d-separate X from Y on graph G, written (X ⊥ Y | Z)G , if and only if Z blocks every

path from a vertex [variable] in X to a vertex [variable] in Y.

Geiger, Verma and Pearl (1990) show that there is a one-to-one correspondence between the set

of conditional independencies, X ⊥ Y | Z, implied by the above factorization and the set of

triples, X, Y, Z, that satisfy the d-separation criterion in graph G. If G is a directed acyclic graph

with vertex set V, if A and B are in V and if H is also in V, then G linearly implies the

correlation between A and B conditional on H is zero if and only if A and B are d-separated

given H.

The notion of d-separation (directional separation) can be illustrated further. Consider

three variables (vertices): A, B and C. A variable is a collider if arrows converge on it: A B

C. The vertex B is a collider, A and C are d-separated, given the null set. However, if we

condition on B, we open-up the information flow from A to C. Conditioning on B makes A and

C d-connected (directionally connected). Amend the above graph given above to include variable

D, as a child of B, such that:

A → B ← C ↓ D

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If we condition on D rather than B, we, as well, open up the flow between A and C (Pearl, 2000

p.17). This illustrates the (i) component of the definition given above.

If converging arrows do not characterize our information flow, as illustrated above, but if

instead information flow is characterized by diverging arrows, then the d-separation condition is

different. This is given by the (ii) component of the definition above. Say we have three vertices

K, L and M, described by the following graph: K L M. Here L is a common cause of K and

M. The unconditional association (correlation) between K and M will be non-zero, as they have a

common cause L. If we condition on L (know the value of L), the association between K and M

disappears (Pearl, 2000, p.17). Conditioning on common causes blocks the flow of information

between common effects. In an unconditional sense, K and M are d-connected (as they have a

common cause); while conditioning on L, variables K and M are d-separated.

Finally, if our causal path is one of a chain (causal chain), condition (ii) in the above

definition again applies. If D causes E and E causes F, we have the representational flow: D

E F. The unconditional association (correlation) between D and F will be non-zero, but the

association (correlation) between D and F conditional on E will be zero. For causal chains, the

end points (D and F) are not d-separated, while conditioning on the middle vertex (E) makes the

end points d-separated (Pearl, 2000).

Policy and Directed Graphs

Consider the following simple graph on variables X, Y and U, where X represents

GDP/Person, Y represents the percent of a country’s population living on $2/Day or less and U

represents an aggregate of omitted variables, say illiteracy rate, birth rate, percent of the

population judged to be living in a state of under-nourishment, etc.:

X Y U

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Here we observe X and Y in an uncontrolled setting. We are interested in manipulating the

percentage of a country’s population living on two dollars or less per day by manipulating the

level of GDP/capita. In this example, the policy analyst’s task is to study a sample obtained from

a distribution associated with passive observation and predict something about the distribution

that would obtain if a particular policy is imposed (forced on one variable). What values will Y

take on if we force X to take on a value of Xf=x0? (Here we use the notation that X is forced by

way of policy to have a value of x0 as Xf=x0.)

The distinction we want to stress here is that observing X and Y moving together in a

passive sample may not necessarily give us reliable information on how Y will behave when we

actively change X via some policy tool (laws, restrictions, etc.). Pearl (2000) is helpful here by

introducing the “do” operator. The probability of Y, given we see X at x0 (P(Y| see X = x0)) does

not necessarily equal the probability of Y given we set X = x0 (P(Y| do X = x0)). Here Pearl’s

verb “do” has the same interpretation as the verb “force” in the preceding paragraph. The two

cases considered here illustrate Pearl’s distinction between the verbs “seeing” and “doing”.

Consider Table 1, which is a slightly revised version of Table 7.1 in Spirtes, Glymour and

Scheines (2000, page 160). Here Y = 100 -.1 X + U and U is exogenous (has no arrows into it).

The value of Y under passive observation when X = 200, has the same distribution as YXf=200 (Y

when a value of 200 is forced on variable X). In this simple case, inference on the effect of X on

Y under a policy setting on Xf = 200 will be the same as that observed in the unmanipulated (pre-

policy) data, X = 200. In this case Pearl’s “seeing” is a good predictor of Pearl’s “doing.” That is

because X is a parent of Y and there is no backdoor path from X to Y (say via U). So, a policy

analyst may conclude that knowing how X and Y are related in uncontrolled (passive) setting is

sufficient for predicting how they will behave under alternative policy settings.

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On the other hand, consider the graph below, where Y, X and U represent the same

variables as they did in the previous example and V represents an Index of Freedom on each

country:

V

X Y U

Here we have a variable V that causes both X and U. V influences Y indirectly through both X

and U. Accordingly, there exists two ‘paths’ from X to Y: the direct path X Y and the

‘backdoor’ path X V U Y.5 This backdoor path is not blocked by converging arrows

(we do not have, for example, X V U Y).

We summarize this graph with three equations: Y = 100 -.1X + U; X=600-100V; and U =

-5V. Will knowledge of how X and Y behave in passive settings be sufficient for predicting how

they will behave in a policy setting? We might suspect that the answer here is “no”, because

there is a backdoor path (not blocked by converging arrows) from X to Y via V and U.

Consider Table 2 (again a revision of Spirtes, Glymour and Scheines [2000 page 161]).

When X = 200 in the unforced setting our distribution on Y is 60, 60 and 60. However, when we

force X = 200 our distribution on Y is 55, 55, 55, 60, 60,and 60. The distribution of Y when X is

observed to take the value of 200 in a passive setting is different from the distribution of Y when

X is forced to equal 200. Here Pearl’s “seeing” is different from Pearl’s “doing”. Under the

policy setting on X we cannot ignore V, as V influences both X and U. If we used our passive

5 The word “path” refers to any sequence of variables and edges, without regard to direction. Following Pearl (2000, page 79), a set of variables Z satisfying the back-door criteria relative to an ordered pair of variables (Xi , Xj ) in a

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observations on X and Y from table 2, we might say that doubling GDP from $100 per capita to

$200 per capita reduces the percent of people living on $2/day or less by 5 percent (65 - 60

percent). However, by taking account of V, we see that the average reduction in people living at

poverty is 7.5 percent (65 - 57.5 percent).6 We have understated the influence of GDP increases

in reducing poverty because we failed to account for the backdoor path from GDP to poverty

through Freedom (and the omitted variable birth rate). Here is the rule. If we want to predict the

effects of manipulating one variable X on another variable Y, we need be sure that there does not

exist an unblocked backdoor path from X to Y through another variable V. If such a path exists,

we need to condition our prediction of the effects of X on Y on the values of V (For a more

rigorous statement of the rule, see Spirtes, Glymour and Scheines, 2000, Theorem 7.1, page

164).7

Inference on Directed Graphs

Spirtes, Glymour and Scheines (2000) have incorporated the notion of d-separation into an

algorithm (PC Algorithm) for building directed acyclic graphs, using the notion of sepset

(defined below). PC algorithm is an ordered set of commands that begins with a general

unrestricted set of relationships among variables and proceeds step-wise to remove edges

between variables and to direct "causal flow.” The algorithm is described in detail in Spirtes,

Glymour and Scheines (2000). More advanced versions (refinements) are described as the

Modified PC Algorithm, the Causal Inference Algorithm and the Fast Causal Inference

DAG if: (i) no node in Z is a descendant of Xi and (ii) Z blocks every path between Xi and Xj that contains an arrow into Xi. 6 In the passive observation of X and Y case, we conclude that the average GDP/Person change of $100 reduces the percent of people living off of $2/day on average by 5 percent (65 to 60 percent from table 2). In the policy setting we see that under the forced setting of GDP/Person our average poverty percentage is (55 percent+55 +55 percent +60 percent +60 percent +60 percent )/6 = 57.5 percent. So if we were at GDP of $100/Person and considered the effects of changing GDP/Person to $200, we would predict a change in percent living on $2/day to drop to 60 percent, when in fact it would drop to 57.5 percent.

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Algorithm. Scheines, et al., 1994 have incorporated these in software distributed under the name

TETRAD II, which we use in this paper. We restrict our discussion to the PC algorithm, as it is

the most basic and easily understood version (in our opinion) of their contribution.

Briefly, when applying PC algorithm, one begins by forming a complete undirected graph

G on the vertex set V. The complete undirected graph shows an undirected edge between every

variable of the system (every variable in V). Edges between variables are removed sequentially

based on zero correlation or partial correlation (conditional correlation). Fisher’s z-statistic is

used to test whether conditional correlations are significantly different from zero, where

z(ρ(i,j|k)n) = 1/2(n-|k|-3)1/2 x ln{(|1 + ρ(i,j|k)|) x (|1 - ρ(i,j|k)|)-1 }, n is the number of observations

used to estimate the correlations, ρ(i,j|k) is the population correlation between series i and j

conditional on series k (removing the influence of series k on each i and j) and |k| is the number

of variables in k (that we condition on). If i, j and k are normally distributed and r(i,j|k) is the

sample conditional correlation of i and j given k, then the distribution of z(ρ(i,j|k)n) - z(r(i,j|k)n)

is standard normal.

The remaining edges are then directed by using the notion of sepset. The conditioning

variable(s) on removed edges between two variables is called the sepset of the variables whose

edge has been removed (for vanishing zero order conditioning information the sepset is the

empty set). To illustrate, edges are directed by considering triples X Y Z, such that X and

Y are adjacent as are Y and Z, but X and Z are not adjacent. Direct edges between triples:

X Y Z as X → Y ← Z if Y is not in the sepset of X and Z. If X → Y, Y and Z are

adjacent, X and Z are not adjacent and there is no arrowhead at Y, then orient Y Z as Y → Z.

7 Econometricians know this rule from their introductory textbooks as the condition that for an unbiased estimator the right-hand-side variables in a regression equation must not be correlated with the error term, where the error term is the theoretically defined error and not the observed residual from a particular fit model.

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If there is a directed path from X to Y and an edge between X and Y, then direct (X Y) as X

→ Y.

Spirtes et al. (1999) show the connection between directed graphs and the counterfactual

random variable model (the random assignment experimental model) of Holland (1986). First

one needs to have a causally sufficient set of variables. This means that there is (are) no omitted

variable(s) that in fact causes (cause) any two of the included variables under study. If variable

X causes both Y and Z and we leave X out of the analysis, then an apparent causal flow from Y

to Z (or vice versa) may be due to the fact that X causes both Y and Z, so the causal flow

identified as running from Y to Z would be spurious (Suppes, 1970). Second, one needs to

constrain himself (herself) to causal flows that respect a causal Markov condition. That is to say,

if X causes Y and Y causes Z, we can factor the underlying probability distribution on X, Y and

Z as Pr(X,Y,Z) = Pr(X).Pr(Y|X)Pr(Z|Y). In other words, we require causal flows respect a

genealogy condition that one need only condition on parents in order to fully capture the

probability distribution generating any variable. One need not condition on grandparents, uncles

or aunts, or siblings. [Here A is a parent of B if A → B; A is a grandparent of C in the causal

chain A → B → C; D is a sibling of C if B → C and B → D and no causal flow between C and D

exists. The variable C is an uncle (aunt) of E if B → C and B → D and D → E.] Our third

requirement for correspondence between PC algorithm and the randomized experiment is that the

probabilities, Pr, we attempt to capture by graph G are faithful to G if X and Y are dependent if

and only of there is an edge between X and Y.

The Causal Sufficiency, Markov and Faithfulness conditions can be violated. Thus any

result based on observational data must be viewed with caution. The causal sufficiency condition

suggests that one find a sufficiently rich set of theoretically relevant variables upon which to two

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conduct an analysis. Failure to include a relevant variable may lead one to put an edge between

variables when in fact both are effects of an omitted third variable. Failure of the Markov

condition has been noted in quantium mechanical experiments (see Spirtes, Glymour and

Scheines, 2000). Failure to require the condition would require us to ignore statistical

dependency even in experimental designs. Finally, the faithfulness condition can be violated if

parameters between causes happen to be of the correct magnitude to cancel one another.

Scheines et al. (1999, p. 181) illustrate a violation of the faithfulness condition in the

following graph (amended for our use on poverty related variables). Here we write the parameter

values connecting three apparently relevant development variables, life expectancy, under-

nourished and child mortality, as subscripted greek symbols $1, $2 and $3 close to their

respective causal arrows. That is, the betas represent the linear coefficient associated with the

causal relation indicated by the directed edge ( ).

Under-nourished

$1

$2 Child Mortality

$3

Life Expectancy

If $2 = - ($3$1) then the under-nourished and life expectancy are uncorrelated. Thus, we will fail

to place an edge between under-nourished and life expectancy even though the true model

requires one. (This last illustration is a hypothetical causal graph and not meant to represent our

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prior beliefs or our empirical findings. In fact, the expected signs, $1 >0, $2 <0 and $3 <0, make

the violation of faithfulness in this example implausible.)

The faithfullness assumption says that if zero correlations are observed, it is because the

edge is not present and not because of cancelling of deep parameters from the underlying

structural model. Theorists, of course, tell us that such cancellations can arise, as we have just

demonstrated through a constructed example; whether or not such an example can be found in

real world data is another matter. It seems to us that demonstration of such requires either a

random assignment experiment or a priori knowledge of the true model.

This concludes our review of directed graphs and topics related to policy analysis and

causal inference. Below we apply these ideas to thirteen variables associated with poverty.

Data Studied

Poverty measures are discussed in Sen (1981). Economic and physical measures representing

deprivation are considered. The World Bank offers economic measures across a large number of

countries. FAO offers physical measures over a similar set of countries. We use both. The

countries studied are listed in Table 3. The immediate concern this list brings to mind is that we

are not studying all countries. Many “developed” countries are not on our list. This omission

includes countries from Western Europe, North America and the Pacific-rim. Our reason for

exclusion is that both the World Bank economic measures of poverty and the FAO physical

measures of poverty are not available for the entire world. For example, the FAO measure of

undernourishment, given in Table 1 of FAO 2000 page 27, is not given for the United States,

Canada or several European countries; similarly, the World Bank measures on the percent of

population living on $2/day or less are not given for these countries (World Bank, World

Development Report 2000/2001 Box 1.2 page 17 and Table 4 page 280 and 281). Yet, we

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suspect (with probability near one) that some members of these more affluent populations live in

states of economic or physical poverty.

Consequently, there is a selection bias present in our study if we attempt to make

statements with respect to the entire world population. On the other hand, if we constrain

ourselves to making statements on what is generally called the “developing” world (or with

respect to economies in transition), these eighty countries would be prima facie a useful sample.

We include twenty-four countries from sub-Saharan Africa, nineteen of the former Soviet Union

or Eastern European nations, sixteen countries from the Americas, seven countries from North

Africa and the Middle East and five countries from South Asia.

One might question whether South Korea, several eastern European countries and

Portugal should be in our sample as all have poverty rates near zero. Rather than edit the original

World Bank data set, we keep these countries in the sample.

The variables we study are as follows:

$1/Day measure of Poverty. The World Bank’s measure of the percent of each country’s

population living on $1.08 or less per day is our economic measure of extreme poverty where

prices are measured in terms of 1993 purchasing power parity terms. (See World Development

Report 2000/2001 Box 1.2 page 17 and Table 4 page 280 and 281.) The average value of this

measure over our sample is 19.62 percent. The minimum value of less than two percent is

observed for several countries: Algeria, Azerbaijan, Belarus, Bulgaria, Chile, Czech Republic,

Estonia, Georgia, Hungry, Jordan, South Korea, Latvia, Lithuania, Morocco, Poland, Portugal,

Slovak Republic, Slovenia, Thailand, Tunisia and Uruguay. The high value is observed as 72.8

percent in Mali. Other countries for which relatively large values of extreme poverty measure are

observed are: Nigeria (70.2 percent), Central Africa Republic (66.6 percent), Zambia (63.7

percent), Madagascar (63.4 percent), Niger (61.4 percent) and Burkina Faso (61.2 percent).

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$2/Day measure of Poverty. The World Bank’s measure of the percent of each country’s

population living on $2.08 or less per day is a less exclusive measure of economic poverty (less

exclusive than the $1/day measure). Again, prices are measured in terms of 1993 purchasing

power parity terms. (See World Development Report 2000/2001 Box 1.2 page 17 and Table 4

page 280 and 281.) The average value over our eighty countries is 43.15 percent. Nigeria shows

the highest value of 90.8 percent; while several countries show values of less than two percent:

Belarus, Czech Republic, South Korea, Portugal, Slovak Republic and Slovenia. Generally,

African countries dominate the high end of this measure as Niger (85.3 percent), Rwanda (84.6

percent), Central African Republic (84 percent), Mali (90.6 percent), Burkina Faso (85.8

percent), Madagascar (89 percent) and Zambia (87.4 percent), in addition to Nigeria, are joined

only by South Asia countries of India (86.2 percent), Pakistan (84.7 percent) and Nepal (82.5

percent) with percentages in excess of 80 percent. Other Asian countries, Eastern Europe and the

Americas are not at the upper extreme in terms of this measure.

Undernourishment. The FAO measure of undernourishment is based on discrepancies between

the minimum calories required for a population versus the calories available from local food

consumption, trade and stocks (see FAO 2000 page 6 and table 1). The measure is the percentage

of a country’s population whose food intake falls below the minimum requirement. The data are

for years 1996 – 1998. The average value over our eighty countries is 17.51 percent. Low

observations on the index are the Eastern European countries and Portugal all having values less

than 1 percent. Other low observations on this index are South Korea (<1 percent), Tunisia (<1

percent), Turkey (<1 percent) and South Africa (<1 percent). The high observation on

undernourishment is 58 percent in Mozambique. Other high-end observations are noted for

Burkina Faso (50 percent), Ethiopia (49 percent), Kenya (43 percent), Madagascar (40 percent),

Mongolia (45 percent), Niger (46 percent), Sierra Leon (43 percent), Tanzania (41 percent) and

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Zambia (45 percent). The Americas generally measure below 20 percent with respect to

undernourishment, with the Dominican Republic at 28 percent, Guatemala at 24 percent and

Bolivia at 23 percent being the highest measures in the western hemisphere. (Haiti is not part of

our sample. It is part of the FAO study on undernourishment and has a value of 62 percent on

this measure.)

Gini Index. Is the World Bank’s estimate of the extent to which the distribution of income among

individuals or households within a country deviates from equality. A value of 0 indicates

equality across individuals or households. A value of 100 indicates the extreme of inequality.

(See World Development Report 2000/2001 page 320 and Table 5 page 282 and 283.) The

average value on this index for our eighty countries is 40.57. The lowest value (low level of

income inequality) is observed for The Slovak Republic at 19.5. Other low values are observed

for Belarus (21.6), The Czech Republic (26.6), Hungry (27), Latvia (27), Poland (27.2), Romania

(25.5), Slovenia (28.2) and the Ukraine from eastern Europe. Rwanda at 28.9 is the low for

Africa and Bangladesh at 28.3 the low for Asia. The high value for the Gini index is found in

Brazil at 63.4. Other high-end countries with respect to income distribution are Chile (56.5),

Columbia (51.3), Dominican Republic (50.5), El Salvador (50.8), Guatemala (59.6), Honduras

(52.7), Mexico (50.3), Panama (56.6), Paraguay (57.7) and Venezuela (53.8), all from Latin

America. Kenya (57.5), Botswana (50), Mali (50.5), Senegal (54.1), South Africa (58.4) and

Zimbabwe (56.8) are the high-ranking (high levels of income inequality) countries from Africa.

Russia, at 49.6, is the highest among the Eastern European countries.

Un-Freedom Index. The Heritage Foundation’s Index of Freedom is used as a measure of overall

freedoms. The index gives a rating of each country on nine aspects (categories) of “freedom:”

International Trade, Fiscal Burden, Government Intervention, Monetary Policy, Foreign

Investment, Banking and Finance, Wages and Prices, Property Rights and Regulation. Each

17

country is provided a discrete measure of 1, 2, 3, 4 or 5 on each of these categories of freedom.

The integer 1 indicates freedom with respect to a measure; a measure of 5 indicates no freedom

with respect to a measure. Here we use an overall score, the simple average of scores on each of

the nine attributes, rounded to tenths. The index is found at Web site: http://cf.heritage.org

(accessed on April 5, 2001). The mean value on this index is 3.28. The Czech Republic is the

lowest at 2.2 (most free in 1995). Several Latin American countries rank low on this measure

(they measured as relatively free): Bolivia (2.7), Chile (2.55), Costa Rica (2.95), El Salvador

(2.4), Guatemala (2.7), Jamaica (2.8), Panama (2.5), Paraguay (2.8) Peru (2.9), Trinidad and

Tobago (2.6) and Uruguay (2.85). African countries showing low scores were Zambia (2.9),

Tunisia (2.7), Namibia (2.9) and Morocco (2.85). Several European countries, in addition to the

Czech Republic show low values on this index: Estonia (2.3), Latvia (2.85), Poland (2.9),

Portugal (2.65) and Turkey (2.9). Asian countries showing low measures on this index are: Sri

Lanka (2.8), Thailand (2.35) and South Korea (2.3). The highest value observed for the Un-

Freedom index is 4.75, associated with Azerbaijan. Other countries scoring high (low degree of

freedom) are: Belarus (4.0), PR Laos (4.45), Mozambique (4.1), Niger (4.0), Rwanda (4.3),

Turkmenistan (4.2), Uzbekistan (4.5) and Yemen (4.1).

Agricultural Value Added Per Worker. This is the World Bank’s measure of the output of the

agricultural sector less the value of the intermediate inputs. Agriculture includes values from

forestry, fishing and hunting, cultivation of crops and livestock production. Data are measured in

1995 constant U.S. dollars. The average value of this measure for our eighty countries

is $2 226.38. The low value was observed in Mozambique at $121. Other countries achieving

low levels of agricultural income are: Bangladesh ($273), Botswana ($473), Burkina Faso

($158), Central African Republic ($380), China ($316), Ethiopia ($136), Gambia ($233), India

($380), Kenya ($222), Madagascar ($187), Mali ($261), Mauritania ($444), Nepal ($185), Niger

18

($194), Rwanda ($326), Senegal ($317), Sierra Leon ($426), Tanzania ($176) Yemen ($369),

Zambia ($210) and Zimbabwe ($312). The high value for Agricultural Income is observed as

$29 860 for Slovenia. Other high agricultural income countries are: Bulgaria ($5 518), Chile

($5 658), South Korea ($8 914), Portugal ($6 695), Uruguay ($6 657) and Venezuela ($5 083).

GDP per capita. The World Bank’s measure is defined as the domestic product divided by mid-

year population in constant 1995 U.S. dollars. The average value for our sample is ($1 916.4).

Ethiopia shows the lowest levels of 1995 income at $109.8. Other low-income achieving

countries include: Burkina Faso ($244), Mali ($235), Mauritania ($258), Mozambique ($158),

Nepal ($212), Niger ($205), Nigeria ($256), Rwanda ($221), Sierra Leon ($196), Tanzania

($180) and Yemen ($263). The high value of GDP per capita in our sample is $11 467 found in

South Korea. Other countries showing high levels of GDP/capita are: Portugal ($11 202),

Slovenia ($9 743), Uruguay ($5 975), Czech Republic ($5 288), Chile ($4 858), Brazil ($4 482),

Hungry ($4 441) and Trinidad and Tobago ($4 356).

Illiteracy Rate. Here we use The World Bank’s measure of the percentage of people ages 15 and

older that cannot, with understanding, read and write a short straightforward declaration on their

daily life. The average value of this measure is 25.99 percent. The lowest value for this measure

is found at .14 for Kazakhstan. Most other countries of Eastern Europe or the former Soviet

Union achieve low levels on this measure (high levels of literacy): Belarus (<1 percent), Czech

republic (<1 percent), Estonia (<1 percent), Hungry (<1 percent), Latvia (<1 percent), Lithuania

(<1 percent), Poland (<1 percent), Russia (<1 percent), Slovak Republic (<1 percent), Slovenia

(<1 percent) and the Ukraine (<1 percent). The high value is found at 87 percent in Niger. Other

countries having high rates of illiteracy include: Bangladesh (63 percent), Burkina Faso (81

percent), Central Africa Republic (61 percent), Cote d’Ivoire (61 percent), Ethiopia (68 percent),

Gambia (70 percent), PR Lao (59 percent), Mali (68 percent), Mauritania (61 percent),

19

Mozambique (62 percent), Nepal (65 percent), Senegal (68 percent) and Sierra Leon (60

percent). The Americas in our sample generally fall between 10 and 30 percent with low

percentages found in Uruguay (2.8 percent), Chile (5.2 percent) and Costa Rica (5.3 percent).

Life Expectancy. The World Bank’s measure of the number of years a newborn child would live

if current patterns of mortality at the time of birth remain fixed throughout her/his life. The mean

value of life expectation over our eighty countries is 63.3 years. The low value was observed for

Sierra Leon at 35.2 years. Other countries showing low life expectancy include: Burkina Faso

(45 years), Central Africa Republic (48 years), Cote d’Ivoire (48 years), Ethiopia (44 years),

Mali (44 years), Mozambique (45 years), Niger (45.5 years), Rwanda (47.5 years), Tanzania (49

years) and Zambia (43 years). The high expectation of years of life was 76.5 in Costa Rica. Other

countries showing high values for life expectancy include: the eastern European countries with

life expectancies in the high 60s to low 70s years range. The Americas generally show high life

expectancies, again, in the high 60-year to low 70-year range. Sri Lanka at 73 years sets the

South Asia high mark, exceeding India at 63 years, Nepal at 56.3 years, Bangladesh at 58 years

and Pakistan at about 61 years. Southeast Asia has Thailand at 68 years, Indonesia at about 66

years and PR Lao at 54 years. South Korea has a life expectancy of about 71 years.

Rural Population Percentage. This is the World Bank’s measure of the percentage of a country’s

population living in rural areas. It is calculated from the difference between the total population

and the urban population. The mean value of this measure over our eighty countries is 51.45

percent. The low value of this measure is 10 percent found in Uruguay. Other low values are

found in Chile (16 percent), Venezuela (15 percent), Brazil (20 percent), South Korea (22

percent) and Russia (24 percent). The high value for this measure is found at 94.3 percent in

Rwanda. Other countries having large percentages of rural populations are: Burkina Faso (85

percent), Ethiopia (85 percent), Nepal (90 percent), Niger (81 percent) and Thailand (80

20

percent). Eastern European countries generally have about 30 percent of their populations in the

rural sectors: Estonia (30 percent), Latvia (31 percent), Czech Republic (26 percent), Hungry (37

percent), Russia (24 percent), Turkey (31 percent) and Ukraine (33 percent). The Americas, as

we observed above, have some of the lowest percentages of population living in rural areas, but

rates in the 25 – 40 percent range are not uncommon: Bolivia (39 percent), Columbia (28

percent), Ecuador (40 percent), Mexico (26 percent), Peru (29 percent) and Trinidad and Tobago

(28 percent). Even higher rates of rural populations are observed in Guatemala (61 percent),

Honduras (53 percent), Costa Rica (53 percent) Panama (45 percent) and Paraguay (48 percent).

Southeast Asian countries are generally in excess of 60 percent on this measure: PR Laos (79

percent), Indonesia (60 percent) and Thailand (80 percent). South Asia shows similar numbers:

Sri Lanka (78 percent), Pakistan (66 percent) and India (73 percent).

Child Mortality. We use the World Bank’s measure of the probability that a newborn person will

die before reaching age five if subject to current age-specific mortality rates. The number is

expressed as a rate per 1 000 people. The mean value over our sample is 74.52 deaths per 1 000

population. The low observation across our 80 countries is 6.3 found in Slovenia. Other countries

showing low levels of child mortality are: the Czech Republic (7.60/1 000), Portugal

(8.20/1 000), Slovak Republic (10.40/1000), South Korea (11.30/1000), Hungry (11.80/1 000)

and Poland (11.90/1 000). The high observation on Child Mortality is 286/1 000 in Sierra Leon.

Other countries showing high rates of Child Mortality include: Burkina Faso (229/1 000), Mali

(238/1 000), Mozambique (201/1 000), Niger (260/1 000) and Rwanda (202/1 000). Generally,

Africa south of the Sahara shows death rates in excess of 100/1 000 people for children five and

under. Exceptions include: Botswana at 62/1 000 and South Africa at 70/1 000. Namibia shows a

death rate of 100/1 000. The Americas show Child Mortality rates generally less than 50/1 000,

with Peru (55/1 000), Guatemala (57/1 000) and Bolivia (85/1 000) somewhat higher. Sri Lanka

21

shows a much lower rate (19/1 000) than our other South Asia countries, Nepal (117/1 000),

Pakistan (136/1 000) and India (95/1 000). Eastern Europe (as indicated above) shows low rates

of Child Mortality, generally less than 25/1 000. Turkey at 50/1 000 is an exception. Southeast

Asia shows considerable differences in Child Mortality rates. Thailand is at 34/1 000, Indonesia

at 56/1 000 and PR Lao is at 170/1 000.

Foreign Aid. This is measured as official development assistance and net official aid record of

international transfer of financial resources or of goods and services. The number is expressed as

a percentage of gross national income for 1995. The mean value for our foreign aid measure over

our eighty-country sample is 31.47 percent. The low value for this measure was South Korea at

–2.57 percent. Other countries showing low levels of relative foreign aid are: Brazil (1.6

percent), Portugal (0 percent), Uzbekistan (1.2 percent), Venezuela (1.3 percent) and Nigeria (1.8

percent). The high value on foreign aid percentage was observed at 118.42 percent in Cote

d’Ivoire. Other high observations on this measure are: Mauritania (117.97 percent), Rwanda

(114.61 percent), Namibia (91 percent), Jordan (90 percent), Zambia (82 percent) and Mongolia

(81 percent). Africa south of the Sahara shows a mixed picture with respect to foreign aid.

Several countries receive aid in excess of 50 percent of their domestic product: Botswana (60

percent), Central Africa Republic (51 percent), Cote d’Ivoire (118 percent), Gambia (65 percent),

Lesotho (62 percent), Mauritania (118 percent), Mozambique (78 percent), Namibia (91

percent), Rwanda (115 percent), Senegal (79 percent), Zambia (83 percent) and Zimbabwe (52

percent). However, there are many exceptions to this rule: South Africa (7.7 percent), Tanzania

(34 percent), Nigeria (1.8 percent), Niger (43 percent), Mali (47 percent), Madagascar (22

percent), Kenya (26 percent), Ghana (33 percent), Ethiopia (20 percent) and Burkina Faso (44

percent). Eastern Europe generally shows low values on this measure, in a neighborhood of 5 to

20 percent. Notable exceptions on the high side of this range are Poland (47 percent), Armenia

22

(51 percent) and Georgia (33 percent). The Americas observed in this study generally show

measures of foreign aid between 0 and 20 percent of GDP. Exceptions are Bolivia (79 percent),

Honduras (53 percent) and El Salvador (55 percent). South Asia shows values of this measure

less than 33 percent, with India low at 2.5 percent and Sri Lanka high at 33 percent. Southeast

Asia shows low values in Indonesia at 9 percent and Thailand at 10 percent and a relatively high

observation for PR Lao at 48 percent.

International Trade as a percentage of GDP. This measure uses the sum of exports and imports

of goods and services as a share of gross domestic product for the year 1995. The average value

of this measure over our eighty countries is 72 percent. The low value is observed as 16 percent

in Brazil. Other countries achieving low percentages on this measure are: Peru (31 percent),

Rwanda (32 percent) and Bangladesh (30 percent). The high value of this trade measure is 149.9

percent observed in Turkmenistan. Other high-end observations are found in: Estonia (145

percent), Lesotho (144 percent), Jordan (129 percent) and Moldova (129 percent). Generally,

Africa south of the Sahara shows values of this measure less than 75 percent. Exceptions are

Lesotho (as noted above at 144 percent), Botswana (91 percent), Cote d’Ivoire (86 percent),

Gambia (113 percent), Mauritania (103 percent) and Namibia (123 percent). Eastern Europe and

the former Soviet Republics generally show measures of this trade variable in excess of 100

percent. Notable exceptions to this rule are: Poland (50 percent), Turkey (49 percent), Russia (45

percent), Uzbekistan (63 percent), Romania (65 percent), Hungry (79 percent), Portugal (66

percent), Armenia (79 percent), Georgia (46 percent) and Azerbaijan (81 percent). The Americas

generally show measures of this trade variable less than 80 percent; exceptions are Trinidad and

Tobago (93 percent), Jamaica (108 percent), Honduras (99 percent) and Costa Rica (83 percent).

South Asia, Southeast Asia and South Korea show measures less than 100 percent, with Thailand

23

showing the largest Asia observation of 85 percent. North Africa and Middle East countries

generally show less than 100 percent, with Jordan being an exception at 129 percent.

Birth Rate. This measure is the number of live births occurring during the year 1995, per 1 000

population estimated at midyear. The mean value of this measure for our sample of eighty

countries is 27.06/1 000. The low value is observed as 8.6/1 000 in Bulgaria. Other countries

showing low values for this measure are the Eastern European and former Soviet countries, all

less than 15 live births for every 1 000 population. Exceptions to this rule are the Middle

East/South Asia countries: Azerbaijan (18.9/1000), Turkmenistan (28.1/1 000), Kazakhstan

(16.1/1000) and Uzbekistan (29.8/1000). The high value for birth rate was observed as 52.3 in

Niger. Other countries showing high values for this measure are: Ethiopia (47/1 000), Mali

(49/1 000) and Sierra Leon (47/1 000). Generally, Africa south of the Sahara shows birth rates in

excess of 40 live births per 1 000 populations. Notable exceptions to this rule are South Africa

(29/1 000), Zimbabwe (33/1 000), Namibia (37/1 000), Central Africa Republic (38/1 000), Cote

d’Ivoire (38/1 000), Ghana (33/1 000) and Lesotho (36/1 000). The Americas in our sample of

countries generally show birth rates in a neighborhood of 25/1 000. Paraguay (32/1 000),

Guatemala (36/1 000) and Honduras (35/1 000) are somewhat higher. Trinidad and Tobago at

15/1 000 is noticeably lower than the general rule. South Asia shows Nepal and Pakistan in a

neighborhood of 36/1 000; while India (28/1 000) and Sri Lanka (19/1 000) are lower. Southeast

Asia shows PR Loa highest at 41 live births per 1 000 population, Indonesia (24/1 000) and

Thailand (18/1 000) are considerably lower. China and South Korea are in a neighborhood of

16/1 000.

Prior justification for this set of variables comes from several recent studies in

development. Sen (1981) offers discussion on the measurement of poverty and considers both

economic and physical measures. He labels these the income method (the amount of money

24

required to fulfill a minimum basket of survival needs) and the direct method (the actual

consumption basket and its short-fall of some particular requirement). They are related: “… the

income method can be seen as a way of approximating the results of the direct method. However,

the income method can be seen as a way of taking note of individual idiosyncrasies without

upsetting the notion of poverty based on deprivation” (Sen 1881, page 27). The World Bank’s

one and two dollars per day numbers are income measures that allow substitution possibilities (or

idiosyncrasies) of the type to which the above quote refers. On the other hand, the FAO under-

nourished index for each country allows us to consider a basic requirement for food and the

extent that individuals in each country are able to meet that requirement. Requirements of other

goods, such as medical care, while possibly part of one’s general basic requirement set, are not

part of the nutrition requirement (Sen 1981, page 168). The correlation between $2/day and

percent undernourished in our eighty-country data set is .66, indicating a modestly strong

positive association between the two measures.

Citing evidence from the Ethiopian famines it appears as if child mortality is a

particularly strong result of famines. Sen writes: “In Ethiopian famines a high mortality level of

under-five children seems to be a common characteristic.” (Sen page 100 note 27). It is open to

question whether or not this result from an environment of starvation carries-over to less extreme

environments of poverty. Actually, child mortality might well be embedded in a causal chain that

includes several of the measures described above: percent of people living on $1 or $2/day or

less, under-nourishment, birth rate and life expectancy. However, there appears to be questions

as to just where several of these should be placed in this “poverty chain.” For example, should

child mortality be a cause or an effect of birth rate? Empirical evidence suggests a cause, but the

acceptance of the evidence is not unanimous (Williams [1977] and Olsen [1983]).

25

With respect to the child mortality and birth rate question, Berhrman and Deolalikar

write: “ There are two mechanisms through which fertility is influenced by mortality: a

replacement effect whereby a dead infant is replaced ex post by another birth, a hoarding effect

whereby parents respond ex ante to anticipated deaths by bearing more children.” Berhrman and

Deolalokar (1988 page 691). Others have suggested that the empirical evidence cannot

necessarily be accepted because of spurious regression associated with micro mortality and

fertility data. Additional evidence requires use of instrumental variable methods which, when

applied with a priori instruments, in turn generates debate on the proper choice of instruments.

Birdsall writes: “… at the family level high mortality and high fertility may be jointly

determined, so that ordinary least squares estimates will be biased.” (Birdsall 1988, page 518)

The use of instrumental variables requires that one find a set of variables that moves one of the

jointly determined variables without moving the other. In short, use of instrumental variables

requires a directed graph in which we can show that there is a clear partition on variables and

their direction of influence on the jointly determined variables (mortality and fertility).

The nutrition-fertility link has been investigated by Menken et al. (1981). The latter

write: “... little support is provided for the existence of a significant link between food intake and

childbearing in situations of chronic or endemic malnutrition.” (Menken et al. 1981, page 425).

Whether no link exists at more “normal” levels of poverty is open to question.

Life expectancy is a measure of poverty to which other measures in the above described

poverty chain point. Policies related to reductions in under-nutrition, child mortality and the

number of people living on $1 or $2 or less /day are expected (by policy makers) to ultimately

manifest themselves in terms of increases in life expectancy. In the terms of a graphical

representation, we expect to be able to change life expectancy by manipulating nutrition levels,

child mortality and income levels of the extremely poor. Accordingly, we expect to see life

26

expectancy at the end of the causal chain (the poverty chain) running from our measures of

income levels of the extremely poor, nutrition, child mortality and, perhaps, the birth rate.

Our expectation is that several of our variables will precede (come before in a causal

sense) the causal chain described above. GDP, agricultural income (Mellor 1995), freedom

(Sachs and Warner [1997] and Haan and Siermann [1996]), illiteracy (Birdsall 1988, pages 514 -

516) and international trade (Bhagwati [1996] and Edwards [1993]) are expected to cause of one

or more variables of the poverty chain so that one could conceivably manipulate anyone of these

and change one or more of the variables in the chain. On the other hand, we expect that foreign

aid may actually show-up as an effect of poverty. So, it seems that manipulation of one or more

variables in the poverty chain may actually change the level of foreign aid that a country

receives.

Placement of the measure on rural populations is somewhat uncertain as well. Evidence

from famines, especially those in Ethiopia and the Sahel of the early 1970s, as discussed in Sen

Chapters 7 and 8, indicates that pastoralists, cultivators and others living in agricultural

environments were the largest group of destitutes (Sen 1981, pages 101 and 115). More recently,

Rosenzweig writes: “ . . . one important and pervasive characteristic of low-income countries is

the large proportion of the labor force in agriculture.” (Rosenzweig 1988, page 714). Finally,

Demery (1999) shows that during the 1990s in several parts of Africa, rural poverty was more

prevalent than urban poverty. In Burkina Faso, for example, rural poverty (as measured by the

share of population living below the poverty line) is in the neighborhood of 50 percent (fifty

percent of rural dwellers are below the poverty level); while urban poverty is closer to 10 to 15

percent. Similar measures for Zambia are rural dwellers at about 75 percent and urban about 33

percent (see World Bank table 1.3).

27

Mellor (1995) and Timmer (1988) argue that increases in real agricultural incomes are

poverty reducing. Our two measures of agricultural activity, agricultural income and the percent

of the population that is rural are expected to show different relationships to poverty. We expect

that the former will contribute directly to poverty reduction. The role of the latter, as either a

cause or an effect of poverty, seems open to question. Drought effects in an exogenously

determined rural population would be described by the sentence “large rural populations

poverty.” Or are large rural populations a consequence of poverty? Because of a high poverty

rate poor people may relocate to the rural sectors, which would be consistent with the sentence

“poverty large rural populations.”

Because our data are cross-section, we expect to see Foreign Aid to actually be an effect

of one or more variables in that causal chain. Foreign Aid is not set using random assignment

(we do not use experimental methods but observe it [all variables in our study] observationally).

It is itself a function of information signals coming from the less developed world. To see the

long-run effects of foreign aid we would need time series data over several decades.

Figure 1 gives scatter plots of each of twelve variables against the percentage of

population living on two dollars or less per day. We observe from the figure that the Gini Index -

$2/day scatter is quite wide, showing no clear positive or negative relationship between the two

variables. Other visually unclear relationships are the Foreign Aid - $2/day plot and the Trade -

$2/day plot. Positive relationships with our $2/day measure appear in the scatter plots with: the

Index of Un-Freedom, Percentage of the Population that is Rural, Child Mortality, Illiteracy,

Under Nourishment and Birth Rate. Negative relationships appear in the scatter plots between

$2/day or less and Agricultural Income/person and GDP/person.

Figure 2 gives plots similar to Figure 1, except the y-ordinate on each plot is replaced by

the percent of population living on one dollar or less per day. Generally, the plots in Figure 2 are

28

similar to those of Figure 1, except the scatter is lower on the y-axis, reflecting the smaller

percentages of people living on $1/day.

Below we apply TETRAD II to these same data to attempt to sort-out whether any of

these visual relationships are causal.

Results We present results for two different models. First we look at the World Bank’s measure of the

percentage of populations living on two dollars and less per day. This measure is studied with the

twelve related variables discussed above. We then substitute the World Bank’s percentage living

on one dollar per day for the two dollar per day measure so our second set of results refer to the

extreme poor. All other variables are the same in the two sets of results.

Results for Percentages Living on $2 or Less /Day

Our analysis of the two-dollar per day measure begins with the correlation matrix on the

thirteen variables described above. The correlation matrix is the unconditional correlation

between all thirteen variables. We list these in matrix equation (1), labeled V($2). The order in

which the variables are listed is given across the top of the matrix using the abbreviations as

follows: $2 = percent of population living on two dollars or less per day; GI = Gini Index; FR =

Un-Freedom Index; AI = Agricultural Income; LE = Life Expectancy; RU = percent of

population which is rural; CM = Child Mortality; GDP = Gross Domestic Product; IL =

Illiteracy; FA = Foreign Aid; UN= percent of Under-nourished; BR = birth rate and IT =

International Trade. The actual variable definitions are given above.

29

$2 GI FR AI LE RU CM GDP IL FA UN BR IT

( ) ($2)

.

. .. . .. . . .

. . . . .

. . . . . .. . . . . . .

. . . . . . . .

. . . . . . . . .

. . . . . . . .

1

119 136 20 148 13 26 179 09 41 43 1

73 03 38 37 68 181 11 39 40 96 68 161 04 54 72 53 51 51 1

74 07 35 40 80 66 84 49 139 08 16 25 51 31 53 35 42 166 17 39 38 71 62 70 52

V =

−− − −− − −

− − −− −

− − − − −− − −− − −− − − .. .

. . . . . . . . . . .. . . . . . . . . . . .

56 43 182 35 30 45 83 68 87 52 82 50 67 128 19 10 17 24 15 29 09 34 15 24 29 1

− − −− − − − − − − −

The correlations summarized in the first column of the matrix generally agree with our

subjective interpretation of the scatter plots in Figure 1. Strong positive relationships are found

between $2/day and Birth rate (BR) (.82), Child Mortality (CM) (.81), Rural Population (RU)

(.73) and Illiteracy (IL) (.74). Negative relationships between $2/day and Agricultural Income

(AI) (-.48) and domestic income (GDP) (-.61) are modestly strong. However, an even stronger

negative relationship is seen between $2/day and life expectancy (-.79). As several large

correlations are observed in other columns of equation 1 (other than column 1), we might well

expect a rich set of causal flows between and among these variables.

TETRAD II begins with the complete undirected graph in Figure 3. Here every variable

is connected, without direction, to every other variable in the set. Accordingly, each variable has

twelve lines connecting it with the other twelve variables. Lines are removed by way of tests that

the correlation (covariance) between any two variables is not different from zero. If we cannot

reject the hypothesis that a particular correlation (covariance) is zero at some pre-determined

significance level, we remove the line connecting the two variables. TETRAD II considers all

possible correlations between our thirteen variables. (There are n(n-1)/2 = 78 such correlations to

30

consider here, which are given by the off diagonal lower triangular elements of equation (1).)

Edges that remain are said to survive zero order conditioning (as we conditioned on no other

variable to remove edges at this stage). Edges that are removed at zero order conditioning are

given in Table 4, entries 1 through 14. Eight of these removed edges (lines) are with variables

adjacent (connected in Figure 3) to the Gini Index. Four are with variable adjacent to Trade and

two with variables adjacent to the Un-Freedom Index.

Edges (lines connecting variables) surviving these zero order tests are subjected to a

series of first order conditioning tests. Here we condition edges between two variables on a third

variable. If the conditional correlation between any two variables is not significantly different

from zero we remove that edge, just as we did at zero order conditioning. Edges removed at first

order conditioning are given in Table 4, entries 15 through 59. There are 45 edges removed at

first order conditioning. Of these, 17 are from conditioning on Child Mortality, 9 from

conditioning on GDP/Person, 6 each from conditioning on Birth Rate and Life expectancy, 5

from conditioning on percent Under Nourished and 2 from conditioning on percent Living on

Two dollars or less per day. This suggests that Child Mortality is a primary player in

understanding these data. To a somewhat lesser extent, GDP/Person shows itself important.

Continuing on, edges surviving tests of first order conditioning are subjected to tests of

second order conditioning. These are given in Table 4, lines 60 – 65. Of the six edges removed at

second order conditioning, four involve conditioning on birth rate.

TETRAD II cannot remove remaining edges at higher order (i.e. third order and higher)

conditioning. It directs edges using sepset arguments discussed above. The resulting pattern is

given in Figure 4. Arrows indicate direction of causation and a sign indicates whether an increase

in the causal variable will increase (+) or decrease (-) the effect.

31

Here we see something very similar to what we labeled above as “the poverty chain”

running down the center of the figure:

Illiteracy Birth Rate %<$2/day % Pop Rural % Under-nourished Life Expectancy

Income variables (Ag Income/Person and GDP/Person) flow into this chain through their effects

on percent<$2/day. Child Mortality enters the chain through its effect on Birth Rate and Life

Expectancy. Un-Freedom and Income Distribution (Gini Index) enter through their influence on

the Birth Rate. Un-Freedom enters as well through its effects on Income (GDP/Person). Foreign

Aid and International Trade are disconnected from the poverty chain.

Agricultural Income is exogenous, apparently being influenced by the vagaries of nature

(weather) and other (omitted) variables. It feeds directly (with a positive sign) into aggregate

country income (GDP/Person), which in turn causes (with a negative sign) our income-based

poverty measure (percent<$2/day). Both income measures reduce our income-based poverty

measure (thus the negative sign on the edge GDP/Person percent<$2/day). Income enters the

poverty chain at a fairly low level, having no effect on Birth Rates, Child Mortality, or Illiteracy.

A few crucial edge directions require comment. The edge Child Mortality Birth Rate

has been discussed in the literature (see above). Here we see (Table 4) that the edge between the

Gini Index (Income Distribution) and Child Mortality is removed at zero order conditioning, yet

we cannot remove the edge running from the Gini Index to Birth Rate or that running between

Child Mortality and the Birth Rate. Thus by the sepset argument, we direct the triple [Child

Mortality, Birth Rate, Gini Index] as:

Child Mortality Birth Rate Gini Index.

Heretofore, the evidence supporting this direction, Child Mortality Birth Rate, has been based

on time ordered observations. Behrman and Deolalikar write: “ Historically, declines in birth

32

rates have followed periods of mortality decline. This phenomenon, called the Demographic

Transition, took place in Europe during the eighteenth and nineteenth centuries and is evident in

several countries of Latin America and Asia where crude and age-standardized fertility rates

have been falling since the mid-1960s – some two to three decades after the onset of large

mortality declines.” (Behrman and Deolalikar 1989, pages 690-91). TETRAD II finds a similar,

but not time delayed, direction in our cross section data as a result of vanishing unconditional

correlation between Child Mortality and Income Distribution (Gini Index).

The lack of an edge between Life Expectancy and GDP/Person is worth additional

comment as well. Wheeler (1980) studies cross section data and finds a significant effect of Life

Expectancy on GDP using instrumental variables. His choices for instruments are earlier (initial)

values of literacy, life expectancy, calorie availability, etc. He concludes that improvements in

Life Expectancy yield (rather substantial) improvements in GDP. We find the edge between

GDP/Person and Life Expectancy is removed by conditioning on Child Mortality. The p-value

on our removed edge is .12. So we don’t strongly reject that the edge he claims to exist (between

GDP and Life Expectancy) is there. However, if the edge runs in the direction Wheeler suggests,

we would see a directed cycle: GDP Poverty Chain GDP. For cross section data (data

measured at one point in time) this seems difficult to support; although, a dynamic pattern of

feedback with these variables measured with time subscripts, GDPt Poverty Chaint GDPt+k ,

k > 0, is plausible.

Un-Freedom has an effect on the poverty chain through its causal effect on GDP/Person,

which in-turn causes our income-based poverty measure (percent<$2/Day). Notice too that there

is an undirected edge between the Un-Freedom Index and the Gini Index, suggesting the

possibility that these variables are related. Actually in the footnote to Table 6 we report results

33

on the use of Schwarz loss to provide evidence on the direction of this undirected edge. There

we find evidence that the edge may be directed as Un-Freedom Gini Index.

The unattached status of Foreign Aid is interesting. We remove all edges at rather high p-

values, suggesting that the evidence is rather strong that Foreign Aid is not a major player in the

poverty chain. Edges between Foreign Aid and Illiteracy, Child Mortality, Birth Rate,

percent<$2/Day, percent Rural, percent Under-nourished and Life Expectancy are removed with

partial correlations having p-values of .70, .20, .40, .82, .78, .36 and .78, respectively.

Interestingly, the smallest p-value in the above list is that associated with the Child Mortality –

Foreign Aid edge (p = .20). The correlation between these two variables is positive, indicating (if

at all) that increases in Child Mortality lead to higher levels of Foreign Aid. The other small p-

value associated with Foreign Aid, is that associated with the Foreign Aid – Un-Freedom Index.

This edge is removed with a zero-order correlation having a p-value of .15. The sign on the edge

is positive, indicating perhaps that higher levels of Un-Freedom cause higher levels of Foreign

Aid, conceivably reflecting non-poverty related motivations associated with Foreign Aid (in any

case TETRAD II drops the edge, suggesting that the edge is not a major player in the poverty

chain).

International Trade is disconnected to the other variables. Two relatively low p-values on

removed edges with International Trade are those associated with the Agricultural Income –

International Trade edge at .12 and the Illiteracy – International Trade edge at .13. The former is

associated with a positive relationship and the latter associated with a negative relationship. So,

increases in Agricultural Income are associated with higher levels of International Trade and

increases in Illiteracy are associated with decreases in International Trade. One might expect that

if a causal path run between the latter two variables and carries a negative relationship, the path

would run from Illiteracy to International Trade. But, in any case, at a 10 percent significance

34

level we find no links to our measure of International Trade. We expected to see an edge

running from International Trade to GDP/person (following standard trade theory – see Bhagwati

(1996)). This expected edge may show-up in time series data or may be buried in aggregation

over types of trade. The latter including considerations related to the well-known “Dutch

Disease” an empirical observation that countries showing high rates of natural resource exports

also show low rates of income growth (Bessler and Lopes 2001). Several countries in our

sample rely heavily on natural resource exports; e.g. Nigeria, Venezuela and Trinidad.

Results for Percentages Living on $1 or Less /Day

We replicate the graph given above, substituting the $1/Day variable for the $2/Day variable. In

population terms we are studying a much smaller percentage of world population. The

correlation matrix summarizing the linear relationship among the thirteen variables, one of which

is now percent of population living on one dollar or less per day is given in equation (2), labeled

V($1):

$1 GI FR AI LE RU CM GDP IL FA UN BR IT

( ) ($1)

.

. .. . .. . . .

. . . . .

. . . . . .. . . . . . .

. . . . . . . .

. . . . . . . . .

. . . . . . . .

2

124 124 20 137 13 26 180 09 41 43 1

62 03 38 37 68 183 11 39 40 96 68 146 04 54 72 53 51 51 1

68 07 35 40 80 66 84 49 138 08 16 25 51 31 53 35 42 162 17 39 38 71 62 70 52

V =

−− − −− − −

− − −− −

− − − − −− − −− − −− − − .. .

. . . . . . . . . . .. . . . . . . . . . . .

56 43 179 35 30 45 83 68 87 52 82 50 67 121 19 10 17 24 15 29 09 34 15 24 29 1

− − −− − − − − − − −

Notice, that except for the first column V($1) = V($2), twelve of the thirteen variables are the

same. Comparing the first column of equation (1) with the first column equation (2), we see

35

several interesting points. First, the signs on the correlations are the same. Measures that show a

negative (positive) correlation with our $2/day income-based poverty measure show a negative

(positive) correlation with our $1/day measure. However, seemingly large differences show up in

the correlations between our income-based poverty measures and GDP/Person (.18), Un-

Freedom (-.12), Agricultural Income (+.11) and percent of Population Rural (-.11). That is to

say, country to country variation in the percentage of extreme poor (those living on $1/day or

less) is associated less with country to country variation in GDP (-.43), than is the more well-to-

do $2/day measure associated with variation in GDP (-.61). Similarly, variation in Un-Freedom

and our $1/day measure is weaker than variation in Un-Freedom and our $2/day measure (by

.12). Finally, Agricultural Incomes and Percentages of Populations that are Rural are less

associated with our $1/day measure than our $2/day measure.

Figure 5 is the graph associated with equation (2). It is reflective of the differences in

correlations between equation (2) and equation (1). The “poverty chain” found in Figure 4 is

broken at the $1/day measure of poverty. The link to the poverty chain with income levels is

broken also at the $1/day measure. We continue to see the links (edges or lines) between our

non-income poverty variables. TETRAD II cannot direct these as it lacks sufficient information

to provide direction. We still see the causal flows from Child Mortality, Illiteracy and Gini Index

all to Birth Rate. However, in this graph (Figure 5) Birth Rate is a sink, information flows into

Birth Rate but nothing flows out of it. Recall from Figure 4 that we did see a flow from birth rate

to percent Living on $2/day. Via this link, in Figure 4, higher birth rates result in lower life

expectancy. Whereas, in Figure 5 higher birth rates are not causes of lower life expectancy

because the link at $1/day is broken.

Figure 5 generally shows that variation in the measure of extreme poor is detached from

variations in our economic measures, GDP/Person and Agricultural Income/Person. The edge

36

between GDP/Person and $1/Day is removed by conditioning on Child Mortality (this

conditional correlation is -.12 and has a p-value of .54). Similarly, the edge between Agricultural

Income/Person and $1/Day is removed by conditioning on Child Mortality (here the conditional

correlation between Agricultural Income and percent$1/Day is -.07, with a p-value of .55). These

results suggest that the extreme poor are not helped by increasing incomes of the general

population. A contrary result was found for variations in the $2/day poverty measure (Figure 4).

This measure of the more “well-to-do” poor was caused by variation in GDP/Person (and

indirectly by variations in Agricultural Income and Freedom).

Our result on the $1/Day measure and Income measures of the general population don’t

support a “rising tide lifts all boats” interpretation of the macro-income poverty interface –

although simple regressions may suggest otherwise. Consider the following regressions.

Equation (3) is a heteroskedastic-consistent regression (see RATS, Doan 1995) of the percentage

living on one dollar or less per day from country i (percent Onei) on GDP/person from country i

and a constant. The estimated coefficients, standard errors and R2 are given in usual regression

format.

(3) % Onei = 27.45 - .004 (GDP/Person) i ; R2 = .60 (2.65) (.0009)

Here the estimated coefficient associated with GDP/Person is indeed large relative to its

estimated standard error – a t-statistic of 4.65, suggesting at a very low level of significance that

GDP/Person is an important variable in understanding our measure of the extreme poor (percent

One dollar or less per day). The negative sign on the estimated coefficient might well be

interpreted as “when GDP/Person in country i increases, the percentage of the population in

country i living in extreme poverty declines.” Furthermore, one could well design policy to rely

on such a response when world incomes are increasing or decreasing. However, a regression,

37

similar to equation (3), but including Child Mortality on the right-hand-side, yields the following

heteroskedastic-consistent result:

(4) % Onei = 2.75 - .0004 (GDP/Person) i + .237 (Child Mort.)i ; R2 = .84 (2.82) (.0006) (.022)

Focus again on the estimated coefficient on GDP/person and its standard error. The estimate falls

in absolute value relative to the corresponding coefficient from equation (3). Furthermore, the

t-statistic associated with this estimate suggests that at usual levels of significance the coefficient

is not different from zero. Based on results reported in equation (4), we conclude that the

extreme measure of poverty (percent Living on One Dollar or less per day) is not responsive to

changes in GDP/Person.

It is interesting to contrast the results from equations (3) and (4) with analogous

regression equations on the two dollar and less per day poverty measure. Equations (5) and (6)

give corresponding estimated regressions for the Two-dollar per day measure.

(5) % Twoi = 57.96 - .007 (GDP/Person) i ; R2 = .81 (3.39) (.001)

(6) % Twoi = 28.481 - .0033 (GDP/Person) i + .287 (Child Mort.)i ; R2 = .91 (4.223) (.0007) (.0341)

Here the coefficient associated with GDP/Person for country i is significantly different from zero

in both equations (5) and (6). Although its magnitude falls in absolute value in equation (6), it

remains significant (t-statistic of 4.83 in equation (6)). Differences between these last two

regression equations and those found using the one dollar per day measure (equation 3 and 4)

show-up in our directed graphs (Figures 4 and 5) by an arrow running from GDP/person to

$2/day in Figure 4 and no arrow between GDP/person and $1/day in Figure 5.

38

Returning to our discussion of Figure 5, we see that variation in the measure of the

extreme poor do not cause variations in the urban/rural population mix, suggesting that the

extreme poor are not primarily characteristic of rural populations, as are people included in the

$2/day measures. Recall from figure 4 that the $2/day measure is a cause of the percentage of

population living in the rural sector.

The differences between the “extreme poor” and the “moderate poor” are trivially

illustrated in the Venn diagram below. Our results suggest that the inner core (<$1/day) is not

responsive to improvements in the general economic climate of a country. The less extreme poor,

as represented by the outer band, do respond to such improvements. Those in the outer band

move in and out of our poverty classification in response to general economic conditions;

whereas those in the inner core appear to be not responsive to such macro-economic changes.

<$2/day

<$1/day

Furthermore, members of the inner core are less associated with rural environments than are their

less extremely positioned siblings. Both measures of economic poverty are positively related to

Child Mortality, with the $1/day measure showing slightly higher correlation. Recall that the

$2/day measure is indirectly caused by Child Mortality by way of the Birth Rate measure while

the $1/day measure is associated with Child Mortality. TETRAD cannot assign a causal path.

The Child Mortality $1/day possibility is probably less believable than the reverse possibility

Child Mortality $1/day, although an investment view of children may suggest otherwise.

39

Differences between results found from $2/day and $1/day measures of poverty suggest

the inner core of poverty is a “hard core”, showing little possibilities for “manipulation” via

policy, whereas the outer layer does appear to offer opportunities via changes in (manipulations

in) literacy rates, birth rates, freedom, agricultural incomes, general economic conditions and

income distribution.

More Regressions (Elasticities)

As is apparent from the regressions on poverty measures and GDP/Person that we reported

above, if one is interested in a measure of the influence of one or more causal variables on

poverty measures, he/she must be sure to condition on the appropriate set of right-hand side

variables.8 If, for example, we want to measure the effect of agricultural income per capita on

our $2 or less per day poverty measure and we use the graph given in Figure 4 as a guide for

specification, we can perform ordinary least squares regression of $2/day on a constant and

agricultural income, because the latter is exogenous in our thirteen variable model. That is, there

is no backdoor path from agricultural income to our $2/day poverty measure. There are no other

variables to be conditioned on (given our causally sufficient set of thirteen variables) for

unbiased estimation of the effect of agricultural income per capita on the $2/Day poverty

measure. We must be careful, however, not to condition on variables that are the effects of

Agricultural Income. That is, we should not include GDP and Agricultural Income on the right

hand side of a regression equation in order to measure the effect of Agricultural Income on

$2/Day.

Equation (7) gives the ordinary least squares regression estimates of the effects of

Agricultural Income/Person on the $2/Day poverty measure:

8 Pearl addresses this point of proper specification in regression models through his analysis of the adjustment problem (see Pearl 2000, pages 78 – 84 and 353 – 357).

40

(7) $2/Day = 51.73 - .0038 Ag Income/Person ; R2 = .23 (4.34) (.0018)

At usual levels of significance (.05 or .10) we would reject the hypothesis that the coefficient

associated with Agricultural Income is zero. However, if we add GDP/Person to the right hand

side of equation (7), we see that the coefficient associated with Agricultural Income is not

significantly different from zero:

(8) $2/Day = 57.99 - .0007 Ag Income/Person - .0068GDP/Person ; R2 = .37 (3.60) (.0014) (.0018)

Equation (8), if interpreted without the advantage of the causal model given in Figure 4, suggests

that agricultural income per person is not important for changing poverty levels. Of course the

reason for the weak measured influence of Agricultural Income/ Person on $2/Day in this

equation is that the former is a cause of GDP/Person, which in turn causes $2/Day. So

conditioning on GDP/Person blocks the measured affect of Agricultural Income/Person on

$2/Day. Equation (8) is not properly specified for measuring the effect of agricultural income on

poverty; while equation (7) is properly specified.

Our estimate of the effect of GDP/person on the $2/day measure requires either the Un-

Freedom index, the Gini Index or Birth Rate be included on the right-hand-side of an ordinary

least squares equation for unbiased estimation of the effect of GDP/Person on the $2/day poverty

measure because there is an unblocked backdoor path running from GDP/person to $2/day

through the Un-Freedom index, the Gini Index and the birth rate. This path has no converging

arrows on it ( Xi ). Conditioning on either the Gini Index, the Un-Freedom Index or Birth

Rate will block the path from GDP/Person to the $2/Day poverty measure.

41

In Table 6 we give the estimated coefficients associated with ordinary least squares

regression of $2/Day on each of its “causal” variables. The table gives coefficient estimates,

estimated standard errors (in parentheses), the coefficient of determination (R2) and elasticity

estimated with respect to changes of each of the “causal” variables identified in Figure 4. These

elasticities are calculated as follows:

0 $2,Xi = %)$2/day )%)Xi = (bi)(mean Xi)/(mean $2/day),

where bi is the estimated coefficient associated with the regression of $2/day on the variable Xi.

The Xi are: the Gini Index, Un-Freedom Index, Illiteracy Rate, Birth Rate, GDP/Person,

Agricultural Income/Person and Child Mortality Rate.

Because there are two undirected edges in Figure 4, we considered alternative regressions

to measure several of the causal effects, depending on the direction of the causal flow in these

undirected edges (see the footnote to Table 6 for more details). From the table we see that the

highest elasticity (indicating the most influential causal variable) is associated with the Un-

Freedom index. That is to say, $2/day poverty measure is most responsive to changes in the Un-

Freedom (UF) index. Our two estimates (a. 0$2,UF = 1.48 and b. 0$2,UF = 1.70, depending on how

we treat the undirected edge between Un-Freedom and the Gini Index) are interpreted as the

percentage change in the percent of a population living on $2 or less per day due to a one percent

change increase in the Un-Freedom index.9 As the estimates are greater than one, this suggests

that the $2/day poverty measure is quite responsive to changes in the freedom levels.

The $2/day poverty measure is also elastic with respect to changes in the birth rate (BR)

(0$2,BR = 1.16). A 1 percent increase in birth rate results in a 1.16 percent increase in the

percentage of a country’s population living on two dollars or less per day.

9 Based on the Schwarz-loss metrics reported in the footnote to Table 6, we recommend using the regressions (elasticities) associated with the Un-Freedom Gini Index and Illiteracy Child Mortality edges.

42

The order of importance of other variables on the two dollar measure is given as: Gini

Index (GI) (0$2,GI • .64), Child Mortality (CM) (0$2,CM •.52), GDP per person (0$2,GDP •-.37),

Illiteracy Rate (IR) (0$2,IR • .33) and Agricultural Income per person (AI) (0$2,AI • -.21). Here

we report the simple averaged estimated elasticity in cases where we estimated two values to

account for undirected edges in Figure 4 (see Table 6).

The elasticity on Illiteracy Rate is interesting. Note from Figure 4 that TETRAD II

cannot direct the edge between Child Mortality and Illiteracy. If we direct this edge as Illiteracy

Rate Child Mortality, then the simple regression of $2/day on Illiteracy Rate is appropriate

and gives us a coefficient associated with illiteracy of .87. Evaluating the elasticity at the mean

values on $2/day and Illiteracy Rate (43.15 and 25.99, respectively) gives us an estimated

elasticity of .52 (0$2,IR • .52). If we direct the edge between Child Mortality and Illiteracy Rate

as Child Mortality Illiteracy Rate, then a backdoor path exist from Illiteracy Rate to $2/day,

because Child Mortality is a cause of $2/Day through Birth Rate (see Figure 4). This requires us

to condition our estimate of the effect of Illiteracy Rate on $2/day on Child Mortality, giving us

an estimated coefficient on Illiteracy Rate of .25 (and an estimated standard error of .17). Again,

we see, as we did on the $1/Day regressions discussed above, that the differences in coefficient

estimates (Table 6) and estimated elasticities are not trivially related to what variables we put on

the right-hand-side in our regression equations. In this last case our subjective view and the

Schwarz-loss measures reported in the footnote to Table 6 suggest the flow of causality on this

edge runs from Illiteracy Rate to Child Mortality.

Summary and Conclusions

We use recently developed methods of directed acyclic graphs to help sort-out causal patterns

among a set of thirteen measures deemed relevant to the incidence of world poverty. Recently

available cross section measures of the percent of population living on one and two dollars or

43

less per day from eighty low income countries are exposed to a battery of tests of conditional

independence with respect to measures of economic and political freedom, income inequality,

income per person, agricultural income, child mortality, birth rate, life expectancy, relative size

of rural population, illiteracy rate, foreign aid as a percentage of national income, international

trade as a percentage of national income and percent of population which is under nourished.

Results are that our measures of economic and political freedom, income inequality, illiteracy

and agricultural income are exogenous movers of poverty. Results on foreign aid and

international trade show both to be not connected to other variables in the graph.

Differences in the resulting graphs when our measure of poverty is $2/day, as opposed to

$1/Day, indicate that extreme poverty is less accessible to manipulation through intervention.

Furthermore, extreme poverty appears not to be, particularly, a rural phenomenon. Our graphs

support early literature in finding Child Mortality as a cause of Birth Rates and not finding a

relationship between Under-nutrition and Birth Rates.

Our results are based on cross section data from a sample of 80 less developed countries.

Such analysis assumes a basic exchangeability between observations across countries. We argue

that such an assumption is reasonable, at least at first glance. Human beings under similar

circumstances, whether in country A or B, react basically the same way. A preferred approach

would be to allow country differences, so that we could measure whether people in country

(culture) A react differently than people in country B to changes in one or more of our thirteen

poverty related variables. Time series data on our poverty measures would allow us to say more

relative to such questions.

We used recent advances in modeling directed acyclic graphs. These advances have been

built on a tripod of assumptions discussed in the body of the paper: The Causal Sufficiency

Condition, The Causal Markov Condition and the Faithfulness Condition. While all three may be

44

violated in any particular application, it is the first condition that gives us concern. In a study of

an issue as enormous as “world poverty”, the assumption that we have a list of thirteen causally

sufficient variables is controversial. Yet, in the final analysis some type of causal sufficiency

assumption must be made if we are to make progress with observational data.

This brings us to the discussion offered at the beginning of our paper. Even if we agree

that understanding cause and effect is important, and thus we are willing to move beyond an

agnostic view of poverty as explained in our opening paragraph, there is a message to be

communicated. To identify and measure the relative strengths of causes one must consider the

causal mechanism behind their settings. Indeed if each is set according to some random

assignment process, then there is no need for the graphical methods applied here (as discussed in

Holland 1986). However, if randomization is not used to set values of our casual variables (and

our correlation tests strongly suggest that it is not), then inference and policy analysis requires

that we understand the causal mechanism behind all variables we study! Here we need to

condition any inference and subsequent policy on a fully sufficient set of casual variables. This

point is clearly illustrated in our analysis of the causal mechanism behind the $1/day poverty

measures. A causal path running from GDP/Person to percent living on $1 or less /day is shown

to be highly unlikely when we condition on Child Mortality. A policy recommendation based on

such a causal path (GDP/Person $1 or less/day) may suggest that the extremely poor will

benefit from improvements in the general economy, through, perhaps, some ‘trickle down

process’. Such a suggestion (if based solely on this path) is likely specious.

Causal paths identified in this paper (Figures 4 or 5) may vanish as well if other variables

are added to our (assumed) causally sufficient set. This conclusion puts us on weak ground with

respect to edges that remain. (Removed edges, however, remain detached if we add other

variables to our causally sufficient set.). Yet, we see no alternative, short of making over-

45

confident statements about what we know and why we know it. The wisdom in Pratt and

Schlaifer’s advice when assessing the evidence on the ill effects of smoking is worth recalling:

The estimates of the effects of smoking were shown to remain almost unchanged when one concomitant after another was introduced into the analysis, until finally it became much easier to believe that smoking in fact had the effects it seemed to have than to believe that it was merely proxying for some other, as yet undiscovered variable or variables.” (Pratt and Schlaifer 1988 page 45)

A similar evolution of beliefs on the causes and effects of observational poverty is currently

underway. This evolution will involve tolerance with respect to many possible concomitants.

Variables not studied here but certainly worthy of consideration include access to clean water,

aggregate expenditures on health care, agricultural investment and aggregate financial health; the

list of possibilities is seemingly endless. Nevertheless, the a priori rejection of a subset of

variables or the prior assignment of causal flow may inappropriately mask the underlying causal

flows that are present in the data.

46

Table 1. Hypothetical values of X, Y and U under passive observation and policy settings on X

Passive Observations Forced or Policy Induced

X = GDP/person

Y =

% $2/Day

U = Other Variables

Xf = Forced

=200

UXf=200 =

Other Vars.

YXf=200 = % $2/Day

$100 40 -50 200 -50 30 $100 50 -40 200 -40 40 $100 60 -30 200 -30 50 $200 30 -50 200 -50 30 $200 40 -40 200 -40 40 $200 50 -30 200 -30 50

Y = 100 -.1 X + U.

47

Table 2. Hypothetical values of X, Y, V and U under passive observation and policy settings on X

V=Freedom

X =

GDP/person

Y =

% $2/Day

U = Other Variables

Xf = 200

UXf=200 = Other

Variables

YXf=200 =

% $2/Day 5

$100

65

-25

200

-25

55

5 $100 65 -25 200 -25 55 5 $100 65 -25 200 -25 55 4 $200 60 -20 200 -20 60 4 $200 60 -20 200 -20 60 4 $200 60 -20 200 -20 60

Y = 100 -.1X + U; X=600-100V; and U = -5V.

48

Table 3. Countries studied Algeria Honduras Paraguay Armenia Hungry Peru Azerbaijan India Poland Bangladesh Indonesia Portugal Belarus Jamaica Romania Bolivia Jordan Russia Botswana Kazakhstan Rwanda Brazil Kenya Senegal Bulgaria Korea South Sierra Leon Burkina Faso Lao Peoples Demo. Republic Slovak Republic Central African Republic Latvia Slovenia Chile Lesotho South Africa China Lithuania Sri Lanka Columbia Madagascar Tanzania Costa Rica Mali Thailand Cote d’Ivoire Mauritania Trinidad Czech Mexico Tunisia Dominican Republic Moldova Turkey Ecuador Mongolia Turkmstan Egypt Morocco Ukraine El Salvador Mozambique Uruguay Estonia Namibia Uzbekistan Ethiopia Nepal Venezuela Gambia Niger Yemen Georgia Nigeria Zambia Ghana Pakistan Zimbabwe Guatemala Panama Countries listed in this table were selected from 2001 World Bank Development Indicators for which $1/day and $2/day population figures were available; see World Development Report 2000/2001, Table 4, pages 280-81.

49

Table 4. Edges removed on graph construction with percent living on $2 or less per day, correlation or partial correlation and p-values on Ho: value equals zero

Edge Removed Correlation or Partial Correlation Value Probability on Ho: Gini -- Ag Inc rho(Gini, Ag Inc) -0.1266 0.2612 Gini – Life Exp rho(Gini, Life Exp) -0.0920 0.4157 Gini -- % Rural rho(Gini, % Rural) -0.0298 0.7921 Gini -- Child Mort rho(Gini, Child Mort) 0.1103 0.3283 Gini -- GDP/Person rho(Gini, GDP/Person) -0.0416 0.7131 Gini -- Illiteracy rho(Gini, Illiteracy) 0.0709 0.5315 Gini -- Foreign Aid rho(Gini, Foreign Aid) 0.0829 0.4637 Gini – Under-nourish rho(Gini, Under-nourish) 0.1736 0.1222 Unfree – Foreign Aid rho(Unfree,Foreign Aid) 0.1619 0.1501 Unfree -- Trade rho(Unfree, Trade) -0.1005 0.3734 Ag Inc -- Trade rho(Ag Inc, Trade) 0.1749 0.1193 % Rural -- Trade rho(% Rural, Trade) -0.1487 0.1867 GDP/Person -- Trade rho(GDP/Person,Trade) 0.0920 0.4155 Foreign Aid -- Trade rho(Foreign Aid, Trade) 0.1484 0.1873 Life Exp -- Birth Rate rho(Life Exp, Birth rate | Child Mort) 0.0093 0.9347 Life Exp -- Illiteracy rho(Life Exp, Illiteracy | Child Mort) 0.0312 0.7842 Life Exp -- <$2/Day rho(<$2/Day, Life Exp | Child Mort) -0.1199 0.2906 Life Exp -- % Rural rho(Life Exp, % Rural | Child Mort) -0.1183 0.2973 GDP/Person -- Birth rate rho(GDP/Person, Birth rate | Life Exp) -0.1674 0.1388 GDP/Person -- % Rural rho(GDP/Person,% Rural | <$2/Day) -0.1314 0.2464 Life Exp -- Foreign Aid rho(Life Exp, Foreign Aid | Child Mort) -0.0317 0.7808 Child Mort -- GDP/Person rho(Child Mort, GDP/Person | Birth rate) -0.1385 0.2217 GDP/Person -- Illiteracy rho(GDP/Person, Illiteracy | Life Exp) -0.1284 0.2574 <$2/Day -- Ag Inc rho(<$2/Day, Ag Inc |GDP/Person) -0.0838 0.4619 Ag Inc -- Birth rate rho(Ag Inc, Birth rate | GDP/Person) -0.1285 0.2571 Unfree -- Life Exp rho(Unfree, Life Exp | Child Mortality) -0.1292 0.2544 Ag Inc -- Child Mort rho(Ag Inc, Child Mort | GDP/Person) -0.0574 0.6138 Ag Inc -- Illiteracy rho(Ag Inc, Illiteracy | GDP/Person) -0.0731 0.5213 Ag Inc -- % Under-nourish rho(Ag Inc, % Under-nourish |GDP/Person) -0.0117 0.9180 Ag Inc -- % Rural rho(Ag Inc, % Rural | GDP/Person) -0.0021 0.9852 GDP/Person -- Foreign Aid rho(GDP/Person, Foreign Aid | Life Exp) -0.1050 0.3551 Illiteracy -- Trade rho(Illiteracy, Trade | Child Mort) -0.1731 -0.1256 Child Mort -- Trade rho(Child Mort, Trade | Birth rate) -0.0874 0.4428 Birth rate -- Trade rho(Birth rate, Trade | Child Mort) -0.0745 0.5134 <$2/Day -- Trade rho(<$2/Day, Trade | Birth rate) -0.0698 0.5399

50

Table 4. Cont. Edge Removed Correlation or Partial Correlation Value Probability on Ho: Unfree -- Ag Inc rho(Unfree, Ag Inc | % Under-nourish) -0.1289 0.2556 Ag Inc -- Foreign Aid rho(Ag Inc, Foreign Aid | GDP/Person) -0.0023 0.9839 % Under-nourish –Trade rho(% Under-nourish, Trade | Child Mort) -0.0544 0.6330 Gini – Trade rho(Gini, Trade | Birth Rate) -0.0994 0.3816 <$2/Day – Gini rho(<$2/Day, Gini | Birth Rate) -0.1632 0.1495 Life Exp – Trade rho(Life Exp, Trade | % Under-nourish) 0.1066 0.3481 Unfree – Birth rate rho(Unfree, Birth rate | % Under-nourish) 0.0632 0.5794 % Rural -- Foreign Aid rho(% Rural, Foreign Aid | <$2/Day) 0.0313 0.7832 Unfree – Illiteracy rho(Unfree, Illiteracy | % Under-nourish) 0.1794 0.1119 <$2/Day – Illiteracy rho(<$2/Day, Illiteracy | Child Mort) 0.0940 0.4086 Unfree -- % Rural rho(Unfree, % Rural | Child Mort) 0.1675 0.1385 Unfree -- Child Mort rho(Unfree, Child Mort | % Under-nourish) 0.1772 0.1168 Unfree -- % Under-nourish rho(Unfree, % Under-nourish | GDP/Person) 0.1506 0.1839 <$2/Day -- Foreign Aid rho(<$2/Day, Foreign Aid | Birth rate) -0.0254 0.8232 Illiteracy -- Foreign Aid rho(Illiteracy, Foreign Aid | Child Mort) -0.0441 0.6988 % Under-nourish – Foreign Aid

rho(% Under-nourish ,Foreign Aid | Child Mort)

0.1036 0.3618

Ag Inc -- Life Exp rho(Ag Inc, Life Exp| GDP/Person) 0.0788 0.4887 Foreign Aid – Birth rate rho(Foreign Aid, Birth rate | Child Mort) 0.0955 0.4012 Child Mort -- Foreign Aid rho(Child Mort, Foreign Aid | Life Exp) 0.1454 0.1995 Life Exp -- GDP/Person rho(Life Exp, GDP/Person | Child Mort) 0.1749 0.1218 Illiteracy -- % Under-nourish

rho(Illiteracy, % Under-nourish | Child Mort) -0.0606 0.5949

% Under-nourish – Birth rate

rho(% Under-nourish, Birth rate | Child Mort) 0.1745 0.1228

% Rural -- Child Mort rho(% Rural, Child Mort | Life Exp) 0.1530 0.1770 Child Mort -- % Under-nourish

rho(Child Mort, % Under-nourish | Life Exp) 0.0926 0.4155

GDP/Person -- % Under-nourish

rho(GDP/Person,%Under-nourish| Ag Inc, <$2/Day)

-0.1795 0.1142

% Rural – Illiteracy rho(% Rural, Illiteracy | <$2/Day, Birth Rate) 0.1858 0.1017 <$2/Day -- % Under-nourish

rho(<$2/Day, % Under-nourish | Birth Rate, % Rural)

0.1660 0.1450

% Rural – Birth rate rho(% Rural, Birth rate | <$2/Day, % Under-nourish)

0.1350 0.2364

<$2/Day – Illiteracy rho(<$2/Day, Illiteracy | Birth Rate, Child

Mort) 0.0656 0.5673

<$2/Day – Child Mort rho(<$2/Day, Child Mort| Birth Rate, Life Exp)

0.0694 0.5449

51

Table 5. Edges removed on graph construction with percent living on $1 or less per day, correlation or partial correlation and p-values on Ho: value equals zero

Edge Removed Correlation or Partial Correlation Value Probability on Ho: Gini -- Ag Inc rho(Gini, Ag Inc) -0.1266 0.2612 Gini – Life Exp rho(Gini, Life Exp) -0.0920 0.4157 Gini -- % Rural rho(Gini, % Rural) -0.0298 0.7921 Gini -- Child Mort rho(Gini, Child Mort) 0.1103 0.3283 Gini -- GDP/Person rho(Gini, GDP/Person) -0.0416 0.7131 Gini -- Illiteracy rho(Gini, Illiteracy) 0.0709 0.5315 Gini -- Foreign Aid rho(Gini, Foreign Aid) 0.0829 0.4637 Gini – Under-nourish rho(Gini, Under-nourish) 0.1736 0.1222 Unfree – Foreign Aid rho(Unfree,Foreign Aid) 0.1619 0.1501 Unfree -- Trade rho(Unfree, Trade) -0.1005 0.3734 Ag Inc -- Trade rho(Ag Inc, Trade) 0.1749 0.1193 % Rural -- Trade rho(% Rural, Trade) -0.1487 0.1867 GDP/Person -- Trade rho(GDP/Person,Trade) 0.0920 0.4155 Foreign Aid -- Trade rho(Foreign Aid, Trade) 0.1484 0.1873 Life Exp -- Birth Rate rho(Life Exp, Birth rate | Child Mort) 0.0093 0.9347 Life Exp -- Illiteracy rho(Life Exp, Illiteracy | Child Mort) 0.0312 0.7842 Life Exp -- <$1/Day rho(<$1/Day, Life Exp | Child Mort) -0.0601 0.5976 Life Exp -- % Rural rho(Life Exp, % Rural | Child Mort) -0.1183 0.2973 GDP/Person -- Birth rate rho(GDP/Person, Birth rate | Life Exp) -0.1674 0.1388 GDP/Person -- % Rural rho(GDP/Person,% Rural | <$1/Day) -0.1314 0.2464 Life Exp -- Foreign Aid rho(Life Exp, Foreign Aid | Child Mort) -0.0317 0.7808 Child Mort -- GDP/Person rho(Child Mort, GDP/Person | Birth rate) -0.1385 0.2217 GDP/Person -- Illiteracy rho(GDP/Person, Illiteracy | Life Exp) -0.1284 0.2574 <$1/Day – GDP/Person rho(<$1/Day, GDP/Person |Child Mort|) -0.0706 0.5354 Ag Inc -- Birth rate rho(Ag Inc, Birth rate | GDP/Person) -0.1285 0.2571 Unfree -- Life Exp rho(Unfree, Life Exp | Child Mortality) -0.1292 0.2544 Ag Inc -- Child Mort rho(Ag Inc, Child Mort | GDP/Person) -0.0574 0.6138 Ag Inc -- Illiteracy rho(Ag Inc, Illiteracy | GDP/Person) -0.0731 0.5213 Ag Inc -- % Under-nourish rho(Ag Inc, % Under-nourish |GDP/Person) -0.0117 0.9180 Ag Inc -- % Rural rho(Ag Inc, % Rural | GDP/Person) -0.0021 0.9852 <$1/Day – Ag Inc Rho(<$1/Day, Ag Inc | Child Mortality) -0.0682 0.5493 GDP/Person -- Foreign Aid rho(GDP/Person, Foreign Aid | Life Exp) -0.1050 0.3551 Illiteracy -- Trade rho(Illiteracy, Trade | Child Mort) -0.1731 -0.1256 Child Mort -- Trade rho(Child Mort, Trade | Birth rate) -0.0874 0.4428 Birth rate -- Trade rho(Birth rate, Trade | Child Mort) -0.0745 0.5134

52

Table 5. Cont. Edge Removed Correlation or Partial Correlation Value Probability on Ho: Unfree -- Ag Inc rho(Unfree, Ag Inc | % Under-nourish) -0.1289 0.2556 Ag Inc -- Foreign Aid rho(Ag Inc, Foreign Aid | GDP/Person) -0.0023 0.9839 % Under-nourish –Trade rho(% Under-nourish, Trade | Child Mort) -0.0544 0.6330 <$1/Day -- Trade Rho(<$1/Day, Trade | Child Mortality) 0.0585 0.6077 Gini – Trade rho(Gini, Trade | Birth Rate) -0.0994 0.3816 <$1/Day – Gini rho(<$1/Day, Gini | Birth Rate) -0.0672 0.5551 <$1/Day – Unfree rho(<$1/day, Unfree |Child Mort) -0.1562 0.1676 Life Exp – Trade rho(Life Exp, Trade | % Under-nourish) 0.1066 0.3481 Unfree – Birth rate rho(Unfree, Birth rate | % Under-nourish) 0.0632 0.5794 % Rural -- Foreign Aid rho(% Rural, Foreign Aid | Child Mort) -0.0862 0.4490 Unfree – Illiteracy rho(Unfree, Illiteracy | % Under-nourish) 0.1794 0.1119 Unfree -- % Rural rho(Unfree, % Rural | Child Mort) 0.1675 0.1385 <$1/Day – Foreign Aid rho(<$1/Day, Foreign Aid | Child Mort) -0.1190 0.2944 Unfree -- Child Mort rho(Unfree, Child Mort | % Under-nourish) 0.1772 0.1168 Unfree -- % Under-nourish rho(Unfree, % Under-nourish | GDP/Person) 0.1506 0.1839 Illiteracy -- Foreign Aid rho(Illiteracy, Foreign Aid | Child Mort) -0.0441 0.6988 % Under-nourish -- Foreign Aid

rho(% Under-nourish ,Foreign Aid | Child Mort)

0.1036 0.3618

Ag Inc -- Life Exp rho(Ag Inc, Life Exp| GDP/Person) 0.0788 0.4887 Foreign Aid – Birth rate rho(Foreign Aid, Birth rate | Child Mort) 0.0955 0.4012 Child Mort -- Foreign Aid rho(Child Mort, Foreign Aid | Life Exp) 0.1454 0.1995 Life Exp -- GDP/Person rho(Life Exp, GDP/Person | Child Mort) 0.1749 0.1218 Illiteracy -- % Under-nourish

rho(Illiteracy, % Under-nourish | Child Mort) -0.0606 0.5949

<$1/Day – % Rural rho(<$1/Day, % Rural | Child Mort) 0.1381 0.2228 <$1/Day – %Under-nourish

rho(<$1/Day, %Under-nourish | Child Mort) 0.1198 0.2912

% Under-nourish – Birth rate

rho(% Under-nourish, Birth rate | Child Mort) 0.1745 0.1228

<$1/Day – Illiteracy rho(<$2/Day, Illiteracy | Child Mort) -0.0376 0.7413 % Rural -- Child Mort rho(% Rural, Child Mort | Life Exp) 0.1530 0.1770 Child Mort -- % Under-nourish

rho(Child Mort, % Under-nourish | Life Exp) 0.0926 0.4155

GDP/Person -- % Under-nourish

rho(GDP/Person,%Under-nourish | %Rural, Life Exp)

-0.1840 0.1053

% Rural – GDP/Person rho(% Rural, GDP/Person | Illiteracy, % Under-nourish)

-0.1760 0.1218

% Rural -- Illiteracy rho(< % Rural, Illiteracy| Child Mort, Birth Rate)

0.1560 0.1713

% Rural – Birth rate rho(% Rural, Birth rate | <$2/Day, % Under-nourish)

0.1350 0.2364

% Rural – Birth Rate rho(%Rural, Birth Rate | Child Mort,

Illiteracy) 0.1630 0.1526

<$1/Day – Birth Rate rho(<$1/Day, Birth Rate| Child Mortality, Gini Index)

0.1513 0.1845

53

Table 6. Regressions of percentage living on two dollars or less per day on alternative causal (independent) variables

Causal Sub-Graph Independent Variables R2 Elasticity at Mean ________________ ____________________ _____ (with respect to variable listed first) Gini $2/Day Gini .56 .04 .53 (.29) GGiinnii $$22//DDaayy GGiinnii UUnn--FFrreeeeddoomm ..8800 2222..3399 ..2211 ..7755 UUnn--FFrreeeeddoomm ((..2255)) ((55..9988)) Un-Freedom $2/Day Un-Freedom 19.50 .13 1.48 (6.28) UUnn--FFrreeeeddoomm $$22//DDaayy UUnn--FFrreeeeddoomm GGiinnii 2222..3399 ..8800 ..2211 11..7700 GGiinnii ((55..8899)) ((..2255)) Ag Income $2/Day Ag. Income -.0038 .23 -.21 (.0018) GGDDPP//PPeerrssoonn $$22//DDaayy GGDDPP//PPeerrssoonn UUnn--FFrreeeeddoomm --..00007744 22..7744 ..3377 --..3377 UUnn--FFrreeeeddoomm ((..00001155)) ((66..5544)) Illiteracy $2/Day Illiteracy .869 .54 .52 (.076) IIlllliitteerraaccyy $$22//DDaayy Illiteracy Child Mort .. 224477 ..226666 ..6666 ..1155 CChhiilldd MMoorrtt.. ((..116688)) ((..006633))

54

Table 6. Cont Causal Sub-Graph Independent Variables R2 Elasticity at Mean ________________ ____________________ _____ (with respect to variable listed first) Child Mort $2/Day Child Mort. .339 .65 .59 (.033) CChhiilldd MMoorrtt $$22//DDaayy CChhiilldd MMoorrtt.. IIlllliitteerraaccyy ..226666 ..224477 ..6666 ..4455 IIlllliitteerraaccyy ((..006633)) ((..116688)) Birth Rate $2/Day Birth Rate Un-Freedom 1.851 6.899 .68 1.16 Un-Freedom (.15) (4.16) The entries in the table refer to ordinary least squares regression estimates of the parameters associated with the independent variables listed in under the heading “Independent Variables”. Under each variable is listed the coefficient estimate and its estimated standard error (the latter in parentheses). The column headed by the label “R2”

gives the coefficient of determination associated with the regression summarized in the particular row of the table. The column labeled “Elasticity at the Mean” gives the estimate of the %) $2/Day/ %)Xi , where Xi is the variable listed first under the column “Independent Variables” when reading from left to right. The determining factor on whether there are one or more sub-graphs to represent the causal graph between $2/Day and each independent variable is how we treat the undirected edges from Figure 4: Un-Freedom – Gini Index and Illiteracy Rate – Child Mortality. To illustrate the reason we need two “pictures” on say estimating the effect of Gini Index on $2/Day, consider: if the edge between Gini Index and Un-Freedom runs from Gini to Un-Freedom (Gini Un-Freedom) then to estimate the effect of Gini Index on $2/Day we need only simple (ols) regression. However if the edge is reversed (Un-Freedom Gini), then there is a backdoor path Gini Un-Freedom GDP/Person $2/day, which is not blocked by converging arrows. To estimate the effects of Gini on $2/Day, we condition on either Freedom or GDP/Person in the regression of $2/Day on the Gini Index. Of course, there is also the possibility that these undirected edges reflect more subtle causal relationships involving omitted variables (Lauritzen and Richardson (2002)). Following Haigh and Bessler (2003) we scored the causal graph given in Figure 4 under all four alternative directed orderings on the two ambiguous edges found using TETRAD II: Illiteracy – Child Mortality and Un-Freedom – Gini Index. Using a modified Schwarz-loss metric we find the following:

SL1(Illiteracy Child Mortality and Un-Freedom Gini Index) = 1337.9039998 SL2(Child Mortality Illiteracy and Un-Freedom Gini Index) = 1337.9193124 SL3(Illiteracy Child Mortality and Gini Index Un-Freedom ) = 1337.9040202 SL4(Child Mortality Illiteracy and Gini Index Un-Freedom ) = 1337.9193329

Here SLi = (T)×Log(Trace(Gi) ) + (number of regressors)×log(T), i=1,2,3,4; where T is the number of observations used to fit the alternative models (80) and Gi is the residual variance/covariance matrix associated with model i; see Doan page 5-18 for details on the SL measure in general. As we want to minimize SL, the first metric SL1 indicates the best model for these data.

55

Gini Index

% <

$2/

day

10 20 30 40 50 60 70

0

25

50

75

100

Index of Unfreedom

% <

$2/

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1 2 3 4 5

0

25

50

75

100

Ag Prod/Person ($/person)

% <

$2/

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0 2000 4000 6000 8000 10000

0

25

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Life Expectancy (yrs)

% <

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30 40 50 60 70 80

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% Population Rural

% <

$2/

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0 25 50 75 100

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Child Mortality (deaths per 1000 live births)

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0 50 100 150 200 250 300

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GDP/Person ($)

% <

$2/

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0 2000 4000 6000 8000 10000

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Illiteracy Rate (% of Population > 15 yrs)

% <

$2/

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0 25 50 75 100

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Foriegn Aid (% GDP)

% <

$2/

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0 20 40 60 80 100 120

0

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Under Nourished (% poplation)

% <

$2/

day

0 10 20 30 40 50 60

0

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Birth Rate (per 1000 people)

% <

$2/

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0 10 20 30 40 50 60

0

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75

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Trade (% GDP)

% <

$2/

day

0 25 50 75 100 125 150

0

25

50

75

100

Figure 1. Scatter plots of twelve development-relevant variables and the percentage of populations living on two dollar per day or less from 80 less developed countries

56

Gini Index

% <

$1/

day

10 20 30 40 50 60 70

0

25

50

75

100

Index of Unfreedom

% <

$1/

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Ag Prod/Person ($/person)

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% <

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% Population Rural

% <

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0 25 50 75 100

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Child Mortality (deaths per 1000 live births)

% <

$1/

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GDP/Person ($)

% <

$1/

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0 2500 5000 7500 10000

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Illiteracy Rate (% of Population > 15 yrs)

% <

$1/

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0 25 50 75 100

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Foriegn Aid (% GDP)%

< $

1/da

y0 25 50 75 100 125

0

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Under Nourished (% poplation)

% <

$1/

day

0 10 20 30 40 50 60

0

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Birth Rate (per 1000 people)

% <

$1/

day

0 10 20 30 40 50 60

0

25

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100

trade ($/Person)

% <

$1/

day

0 25 50 75 100 125 150

0

25

50

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100

Figure 2. Scatter plots of twelve development-relevant variables and the percentage of

populations living on one dollar or less per day from 80 less developed countries

57

<$2/day Gini Un-Freedom Ag Inc Life Exp % Pop Rural Child Mortality GDP/capita Illiteracy Foreign Aid % Under-nourish Birth Rate International Trade

Figure 3. Complete undirected graph on thirteen development related variables

58

Ag Income Illiteracy Rate Un-Freedom Index

(-) (+) (+) (+) (-)

GDP/Person Child Mortality Rate Gini Index

(+) (+) (-)

Birth Rate

(+)

<$2/day

(+) (-)

International Trade % Population Rural Foreign Aid

(+)

% Under-nourished

(-)

Life Expectancy

Figure 4. Pattern on thirteen development related variables including percentage of

population living on two dollars and less per day, found with TETRAD II algorithm on mid-1990’s data from eighty less developed countries

(The 10 percent significance level is applied for edge removal; the plus or minus (+ or -) associated with each edge is the algebraic sign on the unconditional correlation between the variables (vertices) associated with each edge.)

59

Ag Income Illiteracy Rate Un-Freedom Index

(-) (+) (+) (+) (-)

GDP/Person Child Mortality Rate Gini Index

(+) (+) (+)

Birth Rate

<$1/day

(-)

International Trade % Population Rural Foreign Aid

(+)

% Under-nourished

(-)

Life Expectancy

Figure 5. Pattern on thirteen development related variables, including percentage of

population living on one dollar and less per day, found with TETRAD II algorithm on mid-1990’s data from eighty less developed countries

(The 10 percent significance level is applied for edge removal; the plus or minus (+ or -) associated with each edge are the algebraic sign on the unconditional correlation between the variables (vertices) associated with each edge.)

60

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Appendix Table 1. Data

Country $2/day GIx Free Ag.Inc L.Exp %Rur CldMor Algeria 15.1 38.7 3.5 1820.00 69.60 43.40 39.00 Armenia 34 44.4 3.75 4698.00 72.70 31.10 19.50 Azerbaijan 9.6 36 4.75 767.00 69.00 44.30 22.80 Bangladesh 77.8 28.3 3.5 273.00 58.10 77.70 94.00 Belarus 2 21.6 4 3860.00 68.40 29.80 15.30 Bolivia 51.4 42 2.7 1072.00 61.50 39.30 85.00 Botswana 61.4 50 3.3 473.00 60.80 71.50 62.00 Brazil 25.4 63.4 3.45 4099.00 67.00 20.40 44.00 Bulgaria 21.9 30.8 3.6 5518.00 70.70 31.40 18.70 Burkina 85.8 48.2 3.8 158.00 45.30 84.60 229.00 C. Afr.Rep. 84 40.9 3.28 380.00 47.60 60.90 157.00 Chile 18.4 56.5 2.55 5658.00 75.20 15.60 13.00 China 53.7 41.5 3.5 316.00 69.70 70.30 39.10 Columbia 28.7 51.3 3.05 3426.00 69.80 28.20 30.00 Costa Rica 23.3 46.1 2.95 4733.00 76.50 53.20 14.80 Cote Divor 49.4 36.9 3.5 1004.00 47.60 56.70 180.60 Czech 2 26.6 2.2 4357.00 73.80 25.50 7.60 Dominican Rep. 16 50.5 3.2 2472.00 70.40 38.20 47.00 Ecuador 52.3 46.6 3.1 1710.00 68.10 39.70 39.00 Egypt 52.7 32 3.45 1133.00 65.30 55.60 66.10 El Salvador 54 50.8 2.4 1690.00 69.40 55.00 39.00 Estonia 5.2 39.5 2.3 3664.00 69.80 30.10 13.00 Ethiopia 76.4 40 3.55 136.00 44.10 84.60 175.00 Gambia 84 47.8 3.4 233.00 50.80 71.00 127.00 Georgia 2 37.1 3.95 1833.00 72.50 41.70 21.30 Ghana 74.6 33.9 3.2 554.00 60.00 64.10 104.00 Guatemala 33.8 59.6 2.7 2111.00 64.20 61.40 57.00 Honduras 68.8 52.7 3.3 1018.00 68.70 52.50 48.00 Hungry 7.3 27 3 4906.00 70.60 37.00 11.80 India 86.2 33.8 3.8 380.00 63.10 73.20 95.00 Indonesia 55.3 31.7 3.15 742.00 65.70 60.20 56.00 Jamaica 25.2 41.1 2.8 1426.00 74.40 46.30 26.00 Jordan 7.4 43.4 2.8 1458.00 70.80 28.60 34.00 Kazakhstn 15.3 32.7 3.28 1522.00 64.10 43.60 32.60 Kenya 62.3 57.5 3.35 222.00 52.60 71.40 112.00 Korea s. 2 31.6 2.3 8914.00 71.00 21.80 11.30 Lao Pdr. 73.2 30.4 4.45 554.00 53.50 79.30 170.00 Latvia 8.3 27 2.85 2540.00 69.70 31.00 18.50 Lesotho 65.7 56 3.65 516.00 58.30 76.00 137.00 Lithuania 7.8 33.6 3.45 2833.00 70.40 31.90 13.20 Madagascar 89 43.4 3.25 187.00 53.50 73.50 158.00 Mali 90.6 50.5 3.25 261.00 44.00 73.20 238.00 Mauritania 68.7 42.4 3.75 444.00 52.70 48.80 149.00 Mexico 34.8 50.3 3.1 1705.00 71.50 26.60 38.40 Moldova 38.4 34.4 3.4 1376.00 66.50 53.90 26.50 Mongolia 50 33.2 3.5 1054.00 64.90 39.20 76.00 Morocco 7.5 39.2 2.85 2197.00 64.50 47.90 67.00 Mozambique 78.4 39.6 4.1 121.00 44.60 66.20 201.00 Namibia 55.8 40.9 2.9 1062.00 58.50 71.40 100.50 Nepal 82.5 36.7 3.55 185.00 56.30 89.70 117.00

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Country $2/day GIx Free Ag.Inc L.Exp %Rur CldMor Niger 85.3 36.1 4 194.00 45.50 81.80 260.00 Nigeria 90.8 37.5 3.3 629.00 50.10 60.50 147.00 Pakistan 84.7 31.2 3.15 632.00 60.90 65.70 136.00 Panama 25.1 56.6 2.5 2475.00 74.00 45.00 25.70 Paraguay 49.3 57.7 2.8 3484.00 69.70 47.60 28.00 Peru 41.4 44.9 2.9 1465.00 67.80 29.10 52.00 Poland 2 27.2 2.9 1622.00 73.00 36.30 11.90 Portugal 0 35.6 2.65 6695.00 74.60 43.60 8.20 Romania 27.5 25.5 3.65 2692.00 69.50 45.10 26.40 Russia 25.1 49.6 3.35 2105.00 67.00 24.10 21.20 Rwanda 84.6 28.9 4.3 326.00 47.50 94.30 202.00 Senegal 67.8 54.1 3.7 317.00 51.50 56.20 130.00 Sierra Leone 74.5 40.9 3.5 426.00 35.20 66.70 286.00 Slovak rep 1.7 19.5 3 2814.00 71.80 43.00 10.40 Slovenia 2 28.2 3 29860.00 74.80 49.90 6.30 So Africa 35.8 58.4 3 3486.00 62.90 50.70 70.00 Sri Lanka 45.4 30.1 2.8 746.00 72.60 77.90 19.00 Tanzania 59.7 38.1 3.5 176.00 49.40 73.10 147.00 Thailand 28.2 46.2 2.35 922.00 68.20 80.00 34.00 Trinidad 39 40.3 2.6 2057.00 71.60 28.30 19.40 Tunisia 10 40.2 2.7 2310.00 70.90 38.10 33.00 Turkey 18 41.5 2.9 1808.00 68.30 30.80 50.00 Turkmenistan 59 35.8 4.2 1506.00 65.70 55.50 50.20 Ukraine 45.7 25.7 3.8 1337.00 67.30 32.60 17.10 Uruguay 6.6 42.3 2.85 6657.00 72.60 10.00 19.80 Uzbekistan 26.5 33.3 4.5 1624.00 69.20 61.50 31.10 Venezuela 44.6 53.8 3.4 5083.00 72.80 14.50 25.20 Yemen 45.2 33.4 4.1 369.00 55.00 76.40 102.00 Zambia 87.4 46.2 2.9 210.00 43.10 60.80 188.50 Zimbabwe 64.2 56.8 3.75 312.00 56.10 68.20 107.70

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Country GDP/Per Illt. For Aid Und.Nour BR Trade $1/day Algeria 1498.82 39.8 15.255 5 27.18 54.113 2 Armenia 809.75 2.13 51.035 21 13 79.23 7.8 Azerbaijan 377.68 5 19.401 32 18.9 80.897 2 Bangladesh 326.21 62.7 14.858 38 28.78 29.78 29.1 Belarus 2013.14 0.6 11.552 0.01 9.8 100.409 2 Bolivia 919.80 18.4 78.559 23 34.2 49.856 29.4 Botswana 3502.09 28.1 60.074 27 35.06 90.603 33.3 Brazil 4482.16 17.2 1.608 10 20.32 16.301 9 Bulgaria 1409.47 2.3 18.727 13 8.6 122.708 2 Burkina 244.09 80.9 44.351 14 45.8 39.464 61.2 C. Afr.Rep. 321.11 61.4 51.328 50 37.98 38.363 66.6 Chile 4858.29 5.2 10.801 4 19.7 59.645 2 China 630.19 19.9 2.706 11 17.12 39.903 18.5 Columbia 2403.14 10 2.046 13 25.5 36.044 11 Costa Rica 3419.72 5.3 22.453 6 24.1 83.071 6.9 Cote Divor 746.89 60.6 118.42 14 38 86.003 12.3 Czech 5288.01 0.6 14.343 0.01 9.3 112.129 2 Dom. Rep. 1607.97 18.8 7.865 28 26.16 66.224 3.2 Ecuador 1563.93 10.9 18.864 5 26.32 53.909 20.2 Egypt 1065.82 49.7 47.137 4 27.18 46.136 3.1 El Salvador 1669.42 24.6 54.991 11 28.52 55.007 26 Estonia 3387.42 0.6 29.266 6 9.1 145.704 2 Ethiopia 109.78 67.8 19.512 49 47.08 40.542 31.3 Gambia 340.73 69.5 64.704 16 43.2 113.014 53.7 Georgia 387.39 2.13 32.529 23 11.6 45.706 2 Ghana 385.80 36.2 32.81 10 33.24 71.558 38.8 Guatemala 1473.15 35.6 22.35 24 36.7 40.393 10 Honduras 705.55 29 53.383 22 34.94 99.107 40.5 Hungry 4441.04 0.8 19.539 0.01 11 78.799 2 India 399.51 47.5 2.544 21 28.3 25.363 44.2 Indonesia 1105.46 17 8.586 6 24.14 52.265 7.7 Jamaica 1782.69 15.9 43.69 10 23.27 108.239 3.2 Jordan 1607.98 14.4 90.784 5 33.1 129.194 2 Kazakhstn 1285.43 0.14 3.032 5 16.7 68.99 1.5 Kenya 342.13 24 25.67 43 35.2 69.362 26.5 Korea s. 11467.4 3.2 -2.57 0.01 15.2 63.116 2 Lao Pdr. 398.42 59.03 48.125 29 41.12 63.757 26.3 Latvia 2035.13 0.2 20.625 4 8.6 109.888 2 Lesotho 521.15 19.7 61.506 29 35.74 143.461 43.1 Lithuania 1819.39 0.6 19.175 0.02 11.1 116.527 2 Madagascar 235.30 38.48 22.393 40 43.62 46.324 63.4 Mali 258.38 68.4 46.918 32 48.76 55.785 72.8 Mauritania 470.88 61.2 117.971 13 41.4 103.032 28.6 Mexico 3250.63 10.6 4.745 5 30.177 62.255 12.2 Moldova 672.94 1.9 12.332 11 13 129.184 11.3 Mongolia 425.16 42.74 81.281 45 24.04 91.591 13.9 Morocco 1378.73 57 24.342 5 26.7 55.927 2 Mozambique 157.87 62.4 77.815 58 42.32 46.594 37.9 Namibia 2080.34 22.2 91.247 31 36.88 123.424 34.9 Nepal 212.10 65.2 21.582 28 35.72 58.013 37.7 Niger 205.40 87.1 42.621 46 52.28 40.409 61.4 Nigeria 256.06 45.1 1.76 8 41.56 75.59 70.2

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Country GDP/Per Illt. For Aid Und.Nour BR Trade $1/day Pakistan 506.82 59.9 13.443 20 37.4 40.302 31 Panama 3039.76 9.7 11.829 16 23.5 78.874 10.3 Paraguay 1842.69 8.4 19.79 13 31.82 73.86 19.5 Peru 2293.10 12.5 14.525 18 27 31.24 15.5 Poland 3037.90 0.3 46.851 0.01 11.2 50.129 2 Portugal 11202.8 10.5 0 0.01 10.8 65.887 2 Romania 1466.32 2.5 6.328 0.01 10.5 65.107 2.8 Russia 2209.39 0.6 12.453 6 9.3 45.359 7.1 Rwanda 221.37 43.5 114.612 39 43.54 31.688 35.7 Senegal 549.71 68.1 78.911 23 39.82 73.942 26.3 Sierra Leone 196.37 60 62.61 43 47.06 49.594 57 Slovak rep 3652.90 0.6 14.671 4 11.4 122.011 1.7 Slovenia 9743.52 0.4 15.949 3 9.5 112.113 2 So Africa 3943.33 17 7.696 0.01 28.74 47.724 11.5 Sri Lanka 727.00 10 33.315 25 19.3 78.874 6.6 Tanzania 180.21 31.1 33.527 41 41.84 51.881 19.9 Thailand 3017.38 6.2 9.916 21 17.9 84.712 2 Trinidad 4356.33 7.61 16.92 13 14.85 92.946 12.4 Tunisia 2118.57 36.3 12.035 0.01 20.8 85.784 2 Turkey 2955.34 18.7 2.668 0.01 22.4 48.986 2.4 Turkmenistan 914.23 14 5.674 10 28.1 149.991 20.9 Ukraine 863.43 0.5 5.582 5 9.6 93.857 2.9 Uruguay 5975.21 2.8 23.264 4 17.8 39.642 2 Uzbekistan 716.45 14.21 1.241 11 29.8 63.437 3.3 Venezuela 3461.78 9.4 1.263 16 25.45 57.841 18.7 Yemen 263.33 61 11.499 35 41.6 82.509 15.7 Zambia 401.47 27.7 82.151 45 43.22 70.187 63.7 Zimbabwe 697.66 16 52.007 37 33.04 72.005 36